52.81/14.26 WORST_CASE(Omega(n^1), O(n^1)) 52.81/14.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 52.81/14.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 52.81/14.28 52.81/14.28 52.81/14.28 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 52.81/14.28 52.81/14.28 (0) CpxTRS 52.81/14.28 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 6 ms] 52.81/14.28 (2) CpxTRS 52.81/14.28 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 59 ms] 52.81/14.28 (4) CpxTRS 52.81/14.28 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 19 ms] 52.81/14.28 (6) CdtProblem 52.81/14.28 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 52.81/14.28 (8) CdtProblem 52.81/14.28 (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 52.81/14.28 (10) CdtProblem 52.81/14.28 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 52.81/14.28 (12) CdtProblem 52.81/14.28 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 332 ms] 52.81/14.28 (14) CdtProblem 52.81/14.28 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 69 ms] 52.81/14.28 (16) CdtProblem 52.81/14.28 (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 52.81/14.28 (18) BOUNDS(1, 1) 52.81/14.28 (19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 52.81/14.28 (20) TRS for Loop Detection 52.81/14.28 (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 52.81/14.28 (22) BEST 52.81/14.28 (23) proven lower bound 52.81/14.28 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 52.81/14.28 (25) BOUNDS(n^1, INF) 52.81/14.28 (26) TRS for Loop Detection 52.81/14.28 52.81/14.28 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (0) 52.81/14.28 Obligation: 52.81/14.28 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 52.81/14.28 52.81/14.28 52.81/14.28 The TRS R consists of the following rules: 52.81/14.28 52.81/14.28 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 52.81/14.28 active(__(X, nil)) -> mark(X) 52.81/14.28 active(__(nil, X)) -> mark(X) 52.81/14.28 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 52.81/14.28 active(U12(tt, V)) -> mark(U13(isNeList(V))) 52.81/14.28 active(U13(tt)) -> mark(tt) 52.81/14.28 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 52.81/14.28 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 52.81/14.28 active(U25(tt, V2)) -> mark(U26(isList(V2))) 52.81/14.28 active(U26(tt)) -> mark(tt) 52.81/14.28 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 52.81/14.28 active(U32(tt, V)) -> mark(U33(isQid(V))) 52.81/14.28 active(U33(tt)) -> mark(tt) 52.81/14.28 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 52.81/14.28 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 52.81/14.28 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 52.81/14.28 active(U46(tt)) -> mark(tt) 52.81/14.28 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 52.81/14.28 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 52.81/14.28 active(U55(tt, V2)) -> mark(U56(isList(V2))) 52.81/14.28 active(U56(tt)) -> mark(tt) 52.81/14.28 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 52.81/14.28 active(U62(tt, V)) -> mark(U63(isQid(V))) 52.81/14.28 active(U63(tt)) -> mark(tt) 52.81/14.28 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 52.81/14.28 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 52.81/14.28 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 52.81/14.28 active(U74(tt)) -> mark(tt) 52.81/14.28 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 52.81/14.28 active(U82(tt, V)) -> mark(U83(isNePal(V))) 52.81/14.28 active(U83(tt)) -> mark(tt) 52.81/14.28 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 52.81/14.28 active(U92(tt)) -> mark(tt) 52.81/14.28 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 52.81/14.28 active(isList(nil)) -> mark(tt) 52.81/14.28 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 52.81/14.28 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 52.81/14.28 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 52.81/14.28 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 52.81/14.28 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 52.81/14.28 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 52.81/14.28 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 52.81/14.28 active(isPal(nil)) -> mark(tt) 52.81/14.28 active(isPalListKind(a)) -> mark(tt) 52.81/14.28 active(isPalListKind(e)) -> mark(tt) 52.81/14.28 active(isPalListKind(i)) -> mark(tt) 52.81/14.28 active(isPalListKind(nil)) -> mark(tt) 52.81/14.28 active(isPalListKind(o)) -> mark(tt) 52.81/14.28 active(isPalListKind(u)) -> mark(tt) 52.81/14.28 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 52.81/14.28 active(isQid(a)) -> mark(tt) 52.81/14.28 active(isQid(e)) -> mark(tt) 52.81/14.28 active(isQid(i)) -> mark(tt) 52.81/14.28 active(isQid(o)) -> mark(tt) 52.81/14.28 active(isQid(u)) -> mark(tt) 52.81/14.28 active(__(X1, X2)) -> __(active(X1), X2) 52.81/14.28 active(__(X1, X2)) -> __(X1, active(X2)) 52.81/14.28 active(U11(X1, X2)) -> U11(active(X1), X2) 52.81/14.28 active(U12(X1, X2)) -> U12(active(X1), X2) 52.81/14.28 active(U13(X)) -> U13(active(X)) 52.81/14.28 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 52.81/14.28 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 52.81/14.28 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 52.81/14.28 active(U24(X1, X2, X3)) -> U24(active(X1), X2, X3) 52.81/14.28 active(U25(X1, X2)) -> U25(active(X1), X2) 52.81/14.28 active(U26(X)) -> U26(active(X)) 52.81/14.28 active(U31(X1, X2)) -> U31(active(X1), X2) 52.81/14.28 active(U32(X1, X2)) -> U32(active(X1), X2) 52.81/14.28 active(U33(X)) -> U33(active(X)) 52.81/14.28 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 52.81/14.28 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 52.81/14.28 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 52.81/14.28 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 52.81/14.28 active(U45(X1, X2)) -> U45(active(X1), X2) 52.81/14.28 active(U46(X)) -> U46(active(X)) 52.81/14.28 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 52.81/14.28 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 52.81/14.28 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 52.81/14.28 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 52.81/14.28 active(U55(X1, X2)) -> U55(active(X1), X2) 52.81/14.28 active(U56(X)) -> U56(active(X)) 52.81/14.28 active(U61(X1, X2)) -> U61(active(X1), X2) 52.81/14.28 active(U62(X1, X2)) -> U62(active(X1), X2) 52.81/14.28 active(U63(X)) -> U63(active(X)) 52.81/14.28 active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) 52.81/14.28 active(U72(X1, X2)) -> U72(active(X1), X2) 52.81/14.28 active(U73(X1, X2)) -> U73(active(X1), X2) 52.81/14.28 active(U74(X)) -> U74(active(X)) 52.81/14.28 active(U81(X1, X2)) -> U81(active(X1), X2) 52.81/14.28 active(U82(X1, X2)) -> U82(active(X1), X2) 52.81/14.28 active(U83(X)) -> U83(active(X)) 52.81/14.28 active(U91(X1, X2)) -> U91(active(X1), X2) 52.81/14.28 active(U92(X)) -> U92(active(X)) 52.81/14.28 __(mark(X1), X2) -> mark(__(X1, X2)) 52.81/14.28 __(X1, mark(X2)) -> mark(__(X1, X2)) 52.81/14.28 U11(mark(X1), X2) -> mark(U11(X1, X2)) 52.81/14.28 U12(mark(X1), X2) -> mark(U12(X1, X2)) 52.81/14.28 U13(mark(X)) -> mark(U13(X)) 52.81/14.28 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 52.81/14.28 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 52.81/14.28 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 52.81/14.28 U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3)) 52.81/14.28 U25(mark(X1), X2) -> mark(U25(X1, X2)) 52.81/14.28 U26(mark(X)) -> mark(U26(X)) 52.81/14.28 U31(mark(X1), X2) -> mark(U31(X1, X2)) 52.81/14.28 U32(mark(X1), X2) -> mark(U32(X1, X2)) 52.81/14.28 U33(mark(X)) -> mark(U33(X)) 52.81/14.28 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 52.81/14.28 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 52.81/14.28 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 52.81/14.28 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 52.81/14.28 U45(mark(X1), X2) -> mark(U45(X1, X2)) 52.81/14.28 U46(mark(X)) -> mark(U46(X)) 52.81/14.28 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 52.81/14.28 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 52.81/14.28 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 52.81/14.28 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 52.81/14.28 U55(mark(X1), X2) -> mark(U55(X1, X2)) 52.81/14.28 U56(mark(X)) -> mark(U56(X)) 52.81/14.28 U61(mark(X1), X2) -> mark(U61(X1, X2)) 52.81/14.28 U62(mark(X1), X2) -> mark(U62(X1, X2)) 52.81/14.28 U63(mark(X)) -> mark(U63(X)) 52.81/14.28 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 52.81/14.28 U72(mark(X1), X2) -> mark(U72(X1, X2)) 52.81/14.28 U73(mark(X1), X2) -> mark(U73(X1, X2)) 52.81/14.28 U74(mark(X)) -> mark(U74(X)) 52.81/14.28 U81(mark(X1), X2) -> mark(U81(X1, X2)) 52.81/14.28 U82(mark(X1), X2) -> mark(U82(X1, X2)) 52.81/14.28 U83(mark(X)) -> mark(U83(X)) 52.81/14.28 U91(mark(X1), X2) -> mark(U91(X1, X2)) 52.81/14.28 U92(mark(X)) -> mark(U92(X)) 52.81/14.28 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 52.81/14.28 proper(nil) -> ok(nil) 52.81/14.28 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 52.81/14.28 proper(tt) -> ok(tt) 52.81/14.28 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 52.81/14.28 proper(isPalListKind(X)) -> isPalListKind(proper(X)) 52.81/14.28 proper(U13(X)) -> U13(proper(X)) 52.81/14.28 proper(isNeList(X)) -> isNeList(proper(X)) 52.81/14.28 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U24(X1, X2, X3)) -> U24(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U25(X1, X2)) -> U25(proper(X1), proper(X2)) 52.81/14.28 proper(isList(X)) -> isList(proper(X)) 52.81/14.28 proper(U26(X)) -> U26(proper(X)) 52.81/14.28 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 52.81/14.28 proper(U32(X1, X2)) -> U32(proper(X1), proper(X2)) 52.81/14.28 proper(U33(X)) -> U33(proper(X)) 52.81/14.28 proper(isQid(X)) -> isQid(proper(X)) 52.81/14.28 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 52.81/14.28 proper(U46(X)) -> U46(proper(X)) 52.81/14.28 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 52.81/14.28 proper(U56(X)) -> U56(proper(X)) 52.81/14.28 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 52.81/14.28 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 52.81/14.28 proper(U63(X)) -> U63(proper(X)) 52.81/14.28 proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 52.81/14.28 proper(U73(X1, X2)) -> U73(proper(X1), proper(X2)) 52.81/14.28 proper(isPal(X)) -> isPal(proper(X)) 52.81/14.28 proper(U74(X)) -> U74(proper(X)) 52.81/14.28 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 52.81/14.28 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 52.81/14.28 proper(U83(X)) -> U83(proper(X)) 52.81/14.28 proper(isNePal(X)) -> isNePal(proper(X)) 52.81/14.28 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 52.81/14.28 proper(U92(X)) -> U92(proper(X)) 52.81/14.28 proper(a) -> ok(a) 52.81/14.28 proper(e) -> ok(e) 52.81/14.28 proper(i) -> ok(i) 52.81/14.28 proper(o) -> ok(o) 52.81/14.28 proper(u) -> ok(u) 52.81/14.28 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 52.81/14.28 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 52.81/14.28 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 52.81/14.28 isPalListKind(ok(X)) -> ok(isPalListKind(X)) 52.81/14.28 U13(ok(X)) -> ok(U13(X)) 52.81/14.28 isNeList(ok(X)) -> ok(isNeList(X)) 52.81/14.28 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 52.81/14.28 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 52.81/14.28 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 52.81/14.28 U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3)) 52.81/14.28 U25(ok(X1), ok(X2)) -> ok(U25(X1, X2)) 52.81/14.28 isList(ok(X)) -> ok(isList(X)) 52.81/14.28 U26(ok(X)) -> ok(U26(X)) 52.81/14.28 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 52.81/14.28 U32(ok(X1), ok(X2)) -> ok(U32(X1, X2)) 52.81/14.28 U33(ok(X)) -> ok(U33(X)) 52.81/14.28 isQid(ok(X)) -> ok(isQid(X)) 52.81/14.28 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 52.81/14.28 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 52.81/14.28 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 52.81/14.28 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 52.81/14.28 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 52.81/14.28 U46(ok(X)) -> ok(U46(X)) 52.81/14.28 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 52.81/14.28 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 52.81/14.28 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 52.81/14.28 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 52.81/14.28 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 52.81/14.28 U56(ok(X)) -> ok(U56(X)) 52.81/14.28 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 52.81/14.28 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 52.81/14.28 U63(ok(X)) -> ok(U63(X)) 52.81/14.28 U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)) 52.81/14.28 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 52.81/14.28 U73(ok(X1), ok(X2)) -> ok(U73(X1, X2)) 52.81/14.28 isPal(ok(X)) -> ok(isPal(X)) 52.81/14.28 U74(ok(X)) -> ok(U74(X)) 52.81/14.28 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 52.81/14.28 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 52.81/14.28 U83(ok(X)) -> ok(U83(X)) 52.81/14.28 isNePal(ok(X)) -> ok(isNePal(X)) 52.81/14.28 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 52.81/14.28 U92(ok(X)) -> ok(U92(X)) 52.81/14.28 top(mark(X)) -> top(proper(X)) 52.81/14.28 top(ok(X)) -> top(active(X)) 52.81/14.28 52.81/14.28 S is empty. 52.81/14.28 Rewrite Strategy: FULL 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 52.81/14.28 The following defined symbols can occur below the 0th argument of top: proper, active 52.81/14.28 The following defined symbols can occur below the 0th argument of proper: proper, active 52.81/14.28 The following defined symbols can occur below the 0th argument of active: proper, active 52.81/14.28 52.81/14.28 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 52.81/14.28 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 52.81/14.28 active(__(X, nil)) -> mark(X) 52.81/14.28 active(__(nil, X)) -> mark(X) 52.81/14.28 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 52.81/14.28 active(U12(tt, V)) -> mark(U13(isNeList(V))) 52.81/14.28 active(U13(tt)) -> mark(tt) 52.81/14.28 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 52.81/14.28 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 52.81/14.28 active(U25(tt, V2)) -> mark(U26(isList(V2))) 52.81/14.28 active(U26(tt)) -> mark(tt) 52.81/14.28 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 52.81/14.28 active(U32(tt, V)) -> mark(U33(isQid(V))) 52.81/14.28 active(U33(tt)) -> mark(tt) 52.81/14.28 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 52.81/14.28 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 52.81/14.28 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 52.81/14.28 active(U46(tt)) -> mark(tt) 52.81/14.28 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 52.81/14.28 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 52.81/14.28 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 52.81/14.28 active(U55(tt, V2)) -> mark(U56(isList(V2))) 52.81/14.28 active(U56(tt)) -> mark(tt) 52.81/14.28 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 52.81/14.28 active(U62(tt, V)) -> mark(U63(isQid(V))) 52.81/14.28 active(U63(tt)) -> mark(tt) 52.81/14.28 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 52.81/14.28 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 52.81/14.28 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 52.81/14.28 active(U74(tt)) -> mark(tt) 52.81/14.28 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 52.81/14.28 active(U82(tt, V)) -> mark(U83(isNePal(V))) 52.81/14.28 active(U83(tt)) -> mark(tt) 52.81/14.28 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 52.81/14.28 active(U92(tt)) -> mark(tt) 52.81/14.28 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 52.81/14.28 active(isList(nil)) -> mark(tt) 52.81/14.28 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 52.81/14.28 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 52.81/14.28 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 52.81/14.28 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 52.81/14.28 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 52.81/14.28 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 52.81/14.28 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 52.81/14.28 active(isPal(nil)) -> mark(tt) 52.81/14.28 active(isPalListKind(a)) -> mark(tt) 52.81/14.28 active(isPalListKind(e)) -> mark(tt) 52.81/14.28 active(isPalListKind(i)) -> mark(tt) 52.81/14.28 active(isPalListKind(nil)) -> mark(tt) 52.81/14.28 active(isPalListKind(o)) -> mark(tt) 52.81/14.28 active(isPalListKind(u)) -> mark(tt) 52.81/14.28 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 52.81/14.28 active(isQid(a)) -> mark(tt) 52.81/14.28 active(isQid(e)) -> mark(tt) 52.81/14.28 active(isQid(i)) -> mark(tt) 52.81/14.28 active(isQid(o)) -> mark(tt) 52.81/14.28 active(isQid(u)) -> mark(tt) 52.81/14.28 active(__(X1, X2)) -> __(active(X1), X2) 52.81/14.28 active(__(X1, X2)) -> __(X1, active(X2)) 52.81/14.28 active(U11(X1, X2)) -> U11(active(X1), X2) 52.81/14.28 active(U12(X1, X2)) -> U12(active(X1), X2) 52.81/14.28 active(U13(X)) -> U13(active(X)) 52.81/14.28 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 52.81/14.28 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 52.81/14.28 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 52.81/14.28 active(U24(X1, X2, X3)) -> U24(active(X1), X2, X3) 52.81/14.28 active(U25(X1, X2)) -> U25(active(X1), X2) 52.81/14.28 active(U26(X)) -> U26(active(X)) 52.81/14.28 active(U31(X1, X2)) -> U31(active(X1), X2) 52.81/14.28 active(U32(X1, X2)) -> U32(active(X1), X2) 52.81/14.28 active(U33(X)) -> U33(active(X)) 52.81/14.28 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 52.81/14.28 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 52.81/14.28 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 52.81/14.28 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 52.81/14.28 active(U45(X1, X2)) -> U45(active(X1), X2) 52.81/14.28 active(U46(X)) -> U46(active(X)) 52.81/14.28 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 52.81/14.28 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 52.81/14.28 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 52.81/14.28 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 52.81/14.28 active(U55(X1, X2)) -> U55(active(X1), X2) 52.81/14.28 active(U56(X)) -> U56(active(X)) 52.81/14.28 active(U61(X1, X2)) -> U61(active(X1), X2) 52.81/14.28 active(U62(X1, X2)) -> U62(active(X1), X2) 52.81/14.28 active(U63(X)) -> U63(active(X)) 52.81/14.28 active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) 52.81/14.28 active(U72(X1, X2)) -> U72(active(X1), X2) 52.81/14.28 active(U73(X1, X2)) -> U73(active(X1), X2) 52.81/14.28 active(U74(X)) -> U74(active(X)) 52.81/14.28 active(U81(X1, X2)) -> U81(active(X1), X2) 52.81/14.28 active(U82(X1, X2)) -> U82(active(X1), X2) 52.81/14.28 active(U83(X)) -> U83(active(X)) 52.81/14.28 active(U91(X1, X2)) -> U91(active(X1), X2) 52.81/14.28 active(U92(X)) -> U92(active(X)) 52.81/14.28 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 52.81/14.28 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 52.81/14.28 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 52.81/14.28 proper(isPalListKind(X)) -> isPalListKind(proper(X)) 52.81/14.28 proper(U13(X)) -> U13(proper(X)) 52.81/14.28 proper(isNeList(X)) -> isNeList(proper(X)) 52.81/14.28 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U24(X1, X2, X3)) -> U24(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U25(X1, X2)) -> U25(proper(X1), proper(X2)) 52.81/14.28 proper(isList(X)) -> isList(proper(X)) 52.81/14.28 proper(U26(X)) -> U26(proper(X)) 52.81/14.28 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 52.81/14.28 proper(U32(X1, X2)) -> U32(proper(X1), proper(X2)) 52.81/14.28 proper(U33(X)) -> U33(proper(X)) 52.81/14.28 proper(isQid(X)) -> isQid(proper(X)) 52.81/14.28 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 52.81/14.28 proper(U46(X)) -> U46(proper(X)) 52.81/14.28 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 52.81/14.28 proper(U56(X)) -> U56(proper(X)) 52.81/14.28 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 52.81/14.28 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 52.81/14.28 proper(U63(X)) -> U63(proper(X)) 52.81/14.28 proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)) 52.81/14.28 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 52.81/14.28 proper(U73(X1, X2)) -> U73(proper(X1), proper(X2)) 52.81/14.28 proper(isPal(X)) -> isPal(proper(X)) 52.81/14.28 proper(U74(X)) -> U74(proper(X)) 52.81/14.28 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 52.81/14.28 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 52.81/14.28 proper(U83(X)) -> U83(proper(X)) 52.81/14.28 proper(isNePal(X)) -> isNePal(proper(X)) 52.81/14.28 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 52.81/14.28 proper(U92(X)) -> U92(proper(X)) 52.81/14.28 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (2) 52.81/14.28 Obligation: 52.81/14.28 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 52.81/14.28 52.81/14.28 52.81/14.28 The TRS R consists of the following rules: 52.81/14.28 52.81/14.28 __(mark(X1), X2) -> mark(__(X1, X2)) 52.81/14.28 __(X1, mark(X2)) -> mark(__(X1, X2)) 52.81/14.28 U11(mark(X1), X2) -> mark(U11(X1, X2)) 52.81/14.28 U12(mark(X1), X2) -> mark(U12(X1, X2)) 52.81/14.28 U13(mark(X)) -> mark(U13(X)) 52.81/14.28 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 52.81/14.28 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 52.81/14.28 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 52.81/14.28 U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3)) 52.81/14.28 U25(mark(X1), X2) -> mark(U25(X1, X2)) 52.81/14.28 U26(mark(X)) -> mark(U26(X)) 52.81/14.28 U31(mark(X1), X2) -> mark(U31(X1, X2)) 52.81/14.28 U32(mark(X1), X2) -> mark(U32(X1, X2)) 52.81/14.28 U33(mark(X)) -> mark(U33(X)) 52.81/14.28 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 52.81/14.28 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 52.81/14.28 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 52.81/14.28 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 52.81/14.28 U45(mark(X1), X2) -> mark(U45(X1, X2)) 52.81/14.28 U46(mark(X)) -> mark(U46(X)) 52.81/14.28 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 52.81/14.28 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 52.81/14.28 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 52.81/14.28 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 52.81/14.28 U55(mark(X1), X2) -> mark(U55(X1, X2)) 52.81/14.28 U56(mark(X)) -> mark(U56(X)) 52.81/14.28 U61(mark(X1), X2) -> mark(U61(X1, X2)) 52.81/14.28 U62(mark(X1), X2) -> mark(U62(X1, X2)) 52.81/14.28 U63(mark(X)) -> mark(U63(X)) 52.81/14.28 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 52.81/14.28 U72(mark(X1), X2) -> mark(U72(X1, X2)) 52.81/14.28 U73(mark(X1), X2) -> mark(U73(X1, X2)) 52.81/14.28 U74(mark(X)) -> mark(U74(X)) 52.81/14.28 U81(mark(X1), X2) -> mark(U81(X1, X2)) 52.81/14.28 U82(mark(X1), X2) -> mark(U82(X1, X2)) 52.81/14.28 U83(mark(X)) -> mark(U83(X)) 52.81/14.28 U91(mark(X1), X2) -> mark(U91(X1, X2)) 52.81/14.28 U92(mark(X)) -> mark(U92(X)) 52.81/14.28 proper(nil) -> ok(nil) 52.81/14.28 proper(tt) -> ok(tt) 52.81/14.28 proper(a) -> ok(a) 52.81/14.28 proper(e) -> ok(e) 52.81/14.28 proper(i) -> ok(i) 52.81/14.28 proper(o) -> ok(o) 52.81/14.28 proper(u) -> ok(u) 52.81/14.28 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 52.81/14.28 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 52.81/14.28 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 52.81/14.28 isPalListKind(ok(X)) -> ok(isPalListKind(X)) 52.81/14.28 U13(ok(X)) -> ok(U13(X)) 52.81/14.28 isNeList(ok(X)) -> ok(isNeList(X)) 52.81/14.28 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 52.81/14.28 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 52.81/14.28 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 52.81/14.28 U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3)) 52.81/14.28 U25(ok(X1), ok(X2)) -> ok(U25(X1, X2)) 52.81/14.28 isList(ok(X)) -> ok(isList(X)) 52.81/14.28 U26(ok(X)) -> ok(U26(X)) 52.81/14.28 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 52.81/14.28 U32(ok(X1), ok(X2)) -> ok(U32(X1, X2)) 52.81/14.28 U33(ok(X)) -> ok(U33(X)) 52.81/14.28 isQid(ok(X)) -> ok(isQid(X)) 52.81/14.28 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 52.81/14.28 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 52.81/14.28 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 52.81/14.28 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 52.81/14.28 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 52.81/14.28 U46(ok(X)) -> ok(U46(X)) 52.81/14.28 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 52.81/14.28 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 52.81/14.28 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 52.81/14.28 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 52.81/14.28 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 52.81/14.28 U56(ok(X)) -> ok(U56(X)) 52.81/14.28 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 52.81/14.28 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 52.81/14.28 U63(ok(X)) -> ok(U63(X)) 52.81/14.28 U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)) 52.81/14.28 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 52.81/14.28 U73(ok(X1), ok(X2)) -> ok(U73(X1, X2)) 52.81/14.28 isPal(ok(X)) -> ok(isPal(X)) 52.81/14.28 U74(ok(X)) -> ok(U74(X)) 52.81/14.28 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 52.81/14.28 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 52.81/14.28 U83(ok(X)) -> ok(U83(X)) 52.81/14.28 isNePal(ok(X)) -> ok(isNePal(X)) 52.81/14.28 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 52.81/14.28 U92(ok(X)) -> ok(U92(X)) 52.81/14.28 top(mark(X)) -> top(proper(X)) 52.81/14.28 top(ok(X)) -> top(active(X)) 52.81/14.28 52.81/14.28 S is empty. 52.81/14.28 Rewrite Strategy: FULL 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 52.81/14.28 Converted rc-obligation to irc-obligation. 52.81/14.28 52.81/14.28 As the TRS is a non-duplicating overlay system, we have rc = irc. 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (4) 52.81/14.28 Obligation: 52.81/14.28 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 52.81/14.28 52.81/14.28 52.81/14.28 The TRS R consists of the following rules: 52.81/14.28 52.81/14.28 __(mark(X1), X2) -> mark(__(X1, X2)) 52.81/14.28 __(X1, mark(X2)) -> mark(__(X1, X2)) 52.81/14.28 U11(mark(X1), X2) -> mark(U11(X1, X2)) 52.81/14.28 U12(mark(X1), X2) -> mark(U12(X1, X2)) 52.81/14.28 U13(mark(X)) -> mark(U13(X)) 52.81/14.28 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 52.81/14.28 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 52.81/14.28 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 52.81/14.28 U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3)) 52.81/14.28 U25(mark(X1), X2) -> mark(U25(X1, X2)) 52.81/14.28 U26(mark(X)) -> mark(U26(X)) 52.81/14.28 U31(mark(X1), X2) -> mark(U31(X1, X2)) 52.81/14.28 U32(mark(X1), X2) -> mark(U32(X1, X2)) 52.81/14.28 U33(mark(X)) -> mark(U33(X)) 52.81/14.28 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 52.81/14.28 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 52.81/14.28 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 52.81/14.28 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 52.81/14.28 U45(mark(X1), X2) -> mark(U45(X1, X2)) 52.81/14.28 U46(mark(X)) -> mark(U46(X)) 52.81/14.28 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 52.81/14.28 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 52.81/14.28 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 52.81/14.28 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 52.81/14.28 U55(mark(X1), X2) -> mark(U55(X1, X2)) 52.81/14.28 U56(mark(X)) -> mark(U56(X)) 52.81/14.28 U61(mark(X1), X2) -> mark(U61(X1, X2)) 52.81/14.28 U62(mark(X1), X2) -> mark(U62(X1, X2)) 52.81/14.28 U63(mark(X)) -> mark(U63(X)) 52.81/14.28 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 52.81/14.28 U72(mark(X1), X2) -> mark(U72(X1, X2)) 52.81/14.28 U73(mark(X1), X2) -> mark(U73(X1, X2)) 52.81/14.28 U74(mark(X)) -> mark(U74(X)) 52.81/14.28 U81(mark(X1), X2) -> mark(U81(X1, X2)) 52.81/14.28 U82(mark(X1), X2) -> mark(U82(X1, X2)) 52.81/14.28 U83(mark(X)) -> mark(U83(X)) 52.81/14.28 U91(mark(X1), X2) -> mark(U91(X1, X2)) 52.81/14.28 U92(mark(X)) -> mark(U92(X)) 52.81/14.28 proper(nil) -> ok(nil) 52.81/14.28 proper(tt) -> ok(tt) 52.81/14.28 proper(a) -> ok(a) 52.81/14.28 proper(e) -> ok(e) 52.81/14.28 proper(i) -> ok(i) 52.81/14.28 proper(o) -> ok(o) 52.81/14.28 proper(u) -> ok(u) 52.81/14.28 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 52.81/14.28 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 52.81/14.28 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 52.81/14.28 isPalListKind(ok(X)) -> ok(isPalListKind(X)) 52.81/14.28 U13(ok(X)) -> ok(U13(X)) 52.81/14.28 isNeList(ok(X)) -> ok(isNeList(X)) 52.81/14.28 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 52.81/14.28 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 52.81/14.28 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 52.81/14.28 U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3)) 52.81/14.28 U25(ok(X1), ok(X2)) -> ok(U25(X1, X2)) 52.81/14.28 isList(ok(X)) -> ok(isList(X)) 52.81/14.28 U26(ok(X)) -> ok(U26(X)) 52.81/14.28 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 52.81/14.28 U32(ok(X1), ok(X2)) -> ok(U32(X1, X2)) 52.81/14.28 U33(ok(X)) -> ok(U33(X)) 52.81/14.28 isQid(ok(X)) -> ok(isQid(X)) 52.81/14.28 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 52.81/14.28 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 52.81/14.28 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 52.81/14.28 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 52.81/14.28 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 52.81/14.28 U46(ok(X)) -> ok(U46(X)) 52.81/14.28 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 52.81/14.28 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 52.81/14.28 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 52.81/14.28 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 52.81/14.28 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 52.81/14.28 U56(ok(X)) -> ok(U56(X)) 52.81/14.28 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 52.81/14.28 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 52.81/14.28 U63(ok(X)) -> ok(U63(X)) 52.81/14.28 U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)) 52.81/14.28 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 52.81/14.28 U73(ok(X1), ok(X2)) -> ok(U73(X1, X2)) 52.81/14.28 isPal(ok(X)) -> ok(isPal(X)) 52.81/14.28 U74(ok(X)) -> ok(U74(X)) 52.81/14.28 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 52.81/14.28 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 52.81/14.28 U83(ok(X)) -> ok(U83(X)) 52.81/14.28 isNePal(ok(X)) -> ok(isNePal(X)) 52.81/14.28 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 52.81/14.28 U92(ok(X)) -> ok(U92(X)) 52.81/14.28 top(mark(X)) -> top(proper(X)) 52.81/14.28 top(ok(X)) -> top(active(X)) 52.81/14.28 52.81/14.28 S is empty. 52.81/14.28 Rewrite Strategy: INNERMOST 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (5) CpxTrsToCdtProof (UPPER BOUND(ID)) 52.81/14.28 Converted Cpx (relative) TRS to CDT 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (6) 52.81/14.28 Obligation: 52.81/14.28 Complexity Dependency Tuples Problem 52.81/14.28 52.81/14.28 Rules: 52.81/14.28 __(mark(z0), z1) -> mark(__(z0, z1)) 52.81/14.28 __(z0, mark(z1)) -> mark(__(z0, z1)) 52.81/14.28 __(ok(z0), ok(z1)) -> ok(__(z0, z1)) 52.81/14.28 U11(mark(z0), z1) -> mark(U11(z0, z1)) 52.81/14.28 U11(ok(z0), ok(z1)) -> ok(U11(z0, z1)) 52.81/14.28 U12(mark(z0), z1) -> mark(U12(z0, z1)) 52.81/14.28 U12(ok(z0), ok(z1)) -> ok(U12(z0, z1)) 52.81/14.28 U13(mark(z0)) -> mark(U13(z0)) 52.81/14.28 U13(ok(z0)) -> ok(U13(z0)) 52.81/14.28 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 52.81/14.28 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 52.81/14.28 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 52.81/14.28 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 52.81/14.28 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 52.81/14.28 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 52.81/14.28 U24(mark(z0), z1, z2) -> mark(U24(z0, z1, z2)) 52.81/14.28 U24(ok(z0), ok(z1), ok(z2)) -> ok(U24(z0, z1, z2)) 52.81/14.28 U25(mark(z0), z1) -> mark(U25(z0, z1)) 52.81/14.28 U25(ok(z0), ok(z1)) -> ok(U25(z0, z1)) 52.81/14.28 U26(mark(z0)) -> mark(U26(z0)) 52.81/14.28 U26(ok(z0)) -> ok(U26(z0)) 52.81/14.28 U31(mark(z0), z1) -> mark(U31(z0, z1)) 52.81/14.28 U31(ok(z0), ok(z1)) -> ok(U31(z0, z1)) 52.81/14.28 U32(mark(z0), z1) -> mark(U32(z0, z1)) 52.81/14.28 U32(ok(z0), ok(z1)) -> ok(U32(z0, z1)) 52.81/14.28 U33(mark(z0)) -> mark(U33(z0)) 52.81/14.28 U33(ok(z0)) -> ok(U33(z0)) 52.81/14.28 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 52.81/14.28 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 52.81/14.28 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 52.81/14.28 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 52.81/14.28 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 52.81/14.28 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 52.81/14.28 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 52.81/14.28 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 52.81/14.28 U45(mark(z0), z1) -> mark(U45(z0, z1)) 52.81/14.28 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 52.81/14.28 U46(mark(z0)) -> mark(U46(z0)) 52.81/14.28 U46(ok(z0)) -> ok(U46(z0)) 52.81/14.28 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 52.81/14.28 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 52.81/14.28 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 52.81/14.28 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 52.81/14.28 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 52.81/14.28 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 52.81/14.28 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 52.81/14.28 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 52.81/14.28 U55(mark(z0), z1) -> mark(U55(z0, z1)) 52.81/14.28 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 52.81/14.28 U56(mark(z0)) -> mark(U56(z0)) 52.81/14.28 U56(ok(z0)) -> ok(U56(z0)) 52.81/14.28 U61(mark(z0), z1) -> mark(U61(z0, z1)) 52.81/14.28 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 52.81/14.28 U62(mark(z0), z1) -> mark(U62(z0, z1)) 52.81/14.28 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 52.81/14.28 U63(mark(z0)) -> mark(U63(z0)) 52.81/14.28 U63(ok(z0)) -> ok(U63(z0)) 52.81/14.28 U71(mark(z0), z1, z2) -> mark(U71(z0, z1, z2)) 52.81/14.28 U71(ok(z0), ok(z1), ok(z2)) -> ok(U71(z0, z1, z2)) 52.81/14.28 U72(mark(z0), z1) -> mark(U72(z0, z1)) 52.81/14.28 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 52.81/14.28 U73(mark(z0), z1) -> mark(U73(z0, z1)) 52.81/14.28 U73(ok(z0), ok(z1)) -> ok(U73(z0, z1)) 52.81/14.28 U74(mark(z0)) -> mark(U74(z0)) 52.81/14.28 U74(ok(z0)) -> ok(U74(z0)) 52.81/14.28 U81(mark(z0), z1) -> mark(U81(z0, z1)) 52.81/14.28 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 52.81/14.28 U82(mark(z0), z1) -> mark(U82(z0, z1)) 52.81/14.28 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 52.81/14.28 U83(mark(z0)) -> mark(U83(z0)) 52.81/14.28 U83(ok(z0)) -> ok(U83(z0)) 52.81/14.28 U91(mark(z0), z1) -> mark(U91(z0, z1)) 52.81/14.28 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 52.81/14.28 U92(mark(z0)) -> mark(U92(z0)) 52.81/14.28 U92(ok(z0)) -> ok(U92(z0)) 52.81/14.28 proper(nil) -> ok(nil) 52.81/14.28 proper(tt) -> ok(tt) 52.81/14.28 proper(a) -> ok(a) 52.81/14.28 proper(e) -> ok(e) 52.81/14.28 proper(i) -> ok(i) 52.81/14.28 proper(o) -> ok(o) 52.81/14.28 proper(u) -> ok(u) 52.81/14.28 isPalListKind(ok(z0)) -> ok(isPalListKind(z0)) 52.81/14.28 isNeList(ok(z0)) -> ok(isNeList(z0)) 52.81/14.28 isList(ok(z0)) -> ok(isList(z0)) 52.81/14.28 isQid(ok(z0)) -> ok(isQid(z0)) 52.81/14.28 isPal(ok(z0)) -> ok(isPal(z0)) 52.81/14.28 isNePal(ok(z0)) -> ok(isNePal(z0)) 52.81/14.28 top(mark(z0)) -> top(proper(z0)) 52.81/14.28 top(ok(z0)) -> top(active(z0)) 52.81/14.28 Tuples: 52.81/14.28 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.28 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.28 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.28 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.28 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.28 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.28 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.28 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.28 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.28 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.28 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.28 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.28 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.28 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.28 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.28 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.28 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.28 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.28 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.28 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.28 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.28 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.28 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.28 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.28 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.28 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.28 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.28 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.28 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.28 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.28 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.28 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.28 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.28 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.28 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.28 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.28 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.28 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.28 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.28 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.28 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.28 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.28 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.28 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.28 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.28 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.28 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.28 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.28 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.28 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.28 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.28 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.28 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.28 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.28 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.28 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.28 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.28 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.28 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.28 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.28 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.28 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.28 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.28 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.28 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.28 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.28 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.28 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.28 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.28 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.28 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.28 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.28 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.28 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.28 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.28 PROPER(nil) -> c75 52.81/14.28 PROPER(tt) -> c76 52.81/14.28 PROPER(a) -> c77 52.81/14.28 PROPER(e) -> c78 52.81/14.28 PROPER(i) -> c79 52.81/14.28 PROPER(o) -> c80 52.81/14.28 PROPER(u) -> c81 52.81/14.28 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.28 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.28 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.28 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.28 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.28 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.28 TOP(mark(z0)) -> c88(TOP(proper(z0)), PROPER(z0)) 52.81/14.28 TOP(ok(z0)) -> c89(TOP(active(z0))) 52.81/14.28 S tuples: 52.81/14.28 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.28 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.28 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.28 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.28 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.28 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.28 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.28 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.28 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.28 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.28 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.28 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.28 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.28 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.28 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.28 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.28 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.28 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.28 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.28 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.28 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.28 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.28 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.28 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.28 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.28 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.28 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.28 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.28 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.28 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.28 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.28 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.28 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.28 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.28 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.28 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.28 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.28 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.28 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.28 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.28 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.28 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.28 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.28 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.28 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.28 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.28 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.28 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.28 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.28 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.28 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.28 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.28 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.28 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.28 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.28 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.28 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.28 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.28 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.28 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.28 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.28 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.28 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.28 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.28 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.28 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.28 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.28 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.28 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.28 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.28 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.28 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.28 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.28 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.28 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.28 PROPER(nil) -> c75 52.81/14.28 PROPER(tt) -> c76 52.81/14.28 PROPER(a) -> c77 52.81/14.28 PROPER(e) -> c78 52.81/14.28 PROPER(i) -> c79 52.81/14.28 PROPER(o) -> c80 52.81/14.28 PROPER(u) -> c81 52.81/14.28 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.28 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.28 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.28 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.28 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.28 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.28 TOP(mark(z0)) -> c88(TOP(proper(z0)), PROPER(z0)) 52.81/14.28 TOP(ok(z0)) -> c89(TOP(active(z0))) 52.81/14.28 K tuples:none 52.81/14.28 Defined Rule Symbols: ___2, U11_2, U12_2, U13_1, U21_3, U22_3, U23_3, U24_3, U25_2, U26_1, U31_2, U32_2, U33_1, U41_3, U42_3, U43_3, U44_3, U45_2, U46_1, U51_3, U52_3, U53_3, U54_3, U55_2, U56_1, U61_2, U62_2, U63_1, U71_3, U72_2, U73_2, U74_1, U81_2, U82_2, U83_1, U91_2, U92_1, proper_1, isPalListKind_1, isNeList_1, isList_1, isQid_1, isPal_1, isNePal_1, top_1 52.81/14.28 52.81/14.28 Defined Pair Symbols: __'_2, U11'_2, U12'_2, U13'_1, U21'_3, U22'_3, U23'_3, U24'_3, U25'_2, U26'_1, U31'_2, U32'_2, U33'_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_3, U72'_2, U73'_2, U74'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_1, PROPER_1, ISPALLISTKIND_1, ISNELIST_1, ISLIST_1, ISQID_1, ISPAL_1, ISNEPAL_1, TOP_1 52.81/14.28 52.81/14.28 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75, c76, c77, c78, c79, c80, c81, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_2, c89_1 52.81/14.28 52.81/14.28 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (7) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 52.81/14.28 Removed 8 trailing nodes: 52.81/14.28 PROPER(o) -> c80 52.81/14.28 PROPER(u) -> c81 52.81/14.28 PROPER(nil) -> c75 52.81/14.28 TOP(ok(z0)) -> c89(TOP(active(z0))) 52.81/14.28 PROPER(a) -> c77 52.81/14.28 PROPER(e) -> c78 52.81/14.28 PROPER(tt) -> c76 52.81/14.28 PROPER(i) -> c79 52.81/14.28 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (8) 52.81/14.28 Obligation: 52.81/14.28 Complexity Dependency Tuples Problem 52.81/14.28 52.81/14.28 Rules: 52.81/14.28 __(mark(z0), z1) -> mark(__(z0, z1)) 52.81/14.28 __(z0, mark(z1)) -> mark(__(z0, z1)) 52.81/14.28 __(ok(z0), ok(z1)) -> ok(__(z0, z1)) 52.81/14.28 U11(mark(z0), z1) -> mark(U11(z0, z1)) 52.81/14.28 U11(ok(z0), ok(z1)) -> ok(U11(z0, z1)) 52.81/14.28 U12(mark(z0), z1) -> mark(U12(z0, z1)) 52.81/14.28 U12(ok(z0), ok(z1)) -> ok(U12(z0, z1)) 52.81/14.28 U13(mark(z0)) -> mark(U13(z0)) 52.81/14.28 U13(ok(z0)) -> ok(U13(z0)) 52.81/14.28 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 52.81/14.28 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 52.81/14.28 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 52.81/14.28 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 52.81/14.28 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 52.81/14.28 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 52.81/14.28 U24(mark(z0), z1, z2) -> mark(U24(z0, z1, z2)) 52.81/14.28 U24(ok(z0), ok(z1), ok(z2)) -> ok(U24(z0, z1, z2)) 52.81/14.28 U25(mark(z0), z1) -> mark(U25(z0, z1)) 52.81/14.28 U25(ok(z0), ok(z1)) -> ok(U25(z0, z1)) 52.81/14.28 U26(mark(z0)) -> mark(U26(z0)) 52.81/14.28 U26(ok(z0)) -> ok(U26(z0)) 52.81/14.28 U31(mark(z0), z1) -> mark(U31(z0, z1)) 52.81/14.28 U31(ok(z0), ok(z1)) -> ok(U31(z0, z1)) 52.81/14.28 U32(mark(z0), z1) -> mark(U32(z0, z1)) 52.81/14.28 U32(ok(z0), ok(z1)) -> ok(U32(z0, z1)) 52.81/14.28 U33(mark(z0)) -> mark(U33(z0)) 52.81/14.28 U33(ok(z0)) -> ok(U33(z0)) 52.81/14.28 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 52.81/14.28 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 52.81/14.28 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 52.81/14.28 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 52.81/14.28 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 52.81/14.28 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 52.81/14.28 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 52.81/14.28 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 52.81/14.28 U45(mark(z0), z1) -> mark(U45(z0, z1)) 52.81/14.28 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 52.81/14.28 U46(mark(z0)) -> mark(U46(z0)) 52.81/14.28 U46(ok(z0)) -> ok(U46(z0)) 52.81/14.28 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 52.81/14.28 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 52.81/14.28 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 52.81/14.28 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 52.81/14.28 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 52.81/14.28 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 52.81/14.28 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 52.81/14.28 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 52.81/14.28 U55(mark(z0), z1) -> mark(U55(z0, z1)) 52.81/14.28 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 52.81/14.28 U56(mark(z0)) -> mark(U56(z0)) 52.81/14.28 U56(ok(z0)) -> ok(U56(z0)) 52.81/14.28 U61(mark(z0), z1) -> mark(U61(z0, z1)) 52.81/14.28 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 52.81/14.28 U62(mark(z0), z1) -> mark(U62(z0, z1)) 52.81/14.28 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 52.81/14.28 U63(mark(z0)) -> mark(U63(z0)) 52.81/14.28 U63(ok(z0)) -> ok(U63(z0)) 52.81/14.28 U71(mark(z0), z1, z2) -> mark(U71(z0, z1, z2)) 52.81/14.28 U71(ok(z0), ok(z1), ok(z2)) -> ok(U71(z0, z1, z2)) 52.81/14.28 U72(mark(z0), z1) -> mark(U72(z0, z1)) 52.81/14.28 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 52.81/14.28 U73(mark(z0), z1) -> mark(U73(z0, z1)) 52.81/14.28 U73(ok(z0), ok(z1)) -> ok(U73(z0, z1)) 52.81/14.28 U74(mark(z0)) -> mark(U74(z0)) 52.81/14.28 U74(ok(z0)) -> ok(U74(z0)) 52.81/14.28 U81(mark(z0), z1) -> mark(U81(z0, z1)) 52.81/14.28 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 52.81/14.28 U82(mark(z0), z1) -> mark(U82(z0, z1)) 52.81/14.28 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 52.81/14.28 U83(mark(z0)) -> mark(U83(z0)) 52.81/14.28 U83(ok(z0)) -> ok(U83(z0)) 52.81/14.28 U91(mark(z0), z1) -> mark(U91(z0, z1)) 52.81/14.28 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 52.81/14.28 U92(mark(z0)) -> mark(U92(z0)) 52.81/14.28 U92(ok(z0)) -> ok(U92(z0)) 52.81/14.28 proper(nil) -> ok(nil) 52.81/14.28 proper(tt) -> ok(tt) 52.81/14.28 proper(a) -> ok(a) 52.81/14.28 proper(e) -> ok(e) 52.81/14.28 proper(i) -> ok(i) 52.81/14.28 proper(o) -> ok(o) 52.81/14.28 proper(u) -> ok(u) 52.81/14.28 isPalListKind(ok(z0)) -> ok(isPalListKind(z0)) 52.81/14.28 isNeList(ok(z0)) -> ok(isNeList(z0)) 52.81/14.28 isList(ok(z0)) -> ok(isList(z0)) 52.81/14.28 isQid(ok(z0)) -> ok(isQid(z0)) 52.81/14.28 isPal(ok(z0)) -> ok(isPal(z0)) 52.81/14.28 isNePal(ok(z0)) -> ok(isNePal(z0)) 52.81/14.28 top(mark(z0)) -> top(proper(z0)) 52.81/14.28 top(ok(z0)) -> top(active(z0)) 52.81/14.28 Tuples: 52.81/14.28 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.28 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.28 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.28 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.28 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.28 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.28 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.28 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.28 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.28 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.28 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.28 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.28 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.28 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.28 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.28 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.28 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.28 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.28 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.28 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.28 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.28 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.28 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.28 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.28 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.28 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.28 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.28 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.28 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.28 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.28 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.28 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.28 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.28 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.28 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.28 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.28 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.28 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.28 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.28 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.28 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.28 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.28 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.28 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.28 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.28 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.28 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.28 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.28 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.28 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.28 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.28 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.28 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.28 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.28 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.28 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.28 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.28 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.28 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.28 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.28 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.28 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.28 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.28 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.28 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.28 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.28 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.28 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.28 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.28 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.28 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.28 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.28 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.28 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.28 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.28 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.28 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.28 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.28 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.28 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.28 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.28 TOP(mark(z0)) -> c88(TOP(proper(z0)), PROPER(z0)) 52.81/14.28 S tuples: 52.81/14.28 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.28 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.28 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.28 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.28 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.28 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.28 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.28 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.28 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.28 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.28 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.28 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.28 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.28 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.28 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.28 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.28 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.28 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.28 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.28 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.28 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.28 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.28 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.28 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.28 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.28 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.28 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.28 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.28 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.28 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.28 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.28 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.28 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.28 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.28 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.28 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.28 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.28 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.28 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.28 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.28 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.28 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.28 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.28 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.28 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.28 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.28 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.28 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.28 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.28 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.28 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.28 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.28 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.28 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.28 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.28 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.28 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.28 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.28 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.28 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.28 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.28 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.28 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.28 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.28 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.28 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.28 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.28 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.28 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.28 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.28 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.28 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.28 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.28 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.28 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.28 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.28 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.28 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.28 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.28 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.28 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.28 TOP(mark(z0)) -> c88(TOP(proper(z0)), PROPER(z0)) 52.81/14.28 K tuples:none 52.81/14.28 Defined Rule Symbols: ___2, U11_2, U12_2, U13_1, U21_3, U22_3, U23_3, U24_3, U25_2, U26_1, U31_2, U32_2, U33_1, U41_3, U42_3, U43_3, U44_3, U45_2, U46_1, U51_3, U52_3, U53_3, U54_3, U55_2, U56_1, U61_2, U62_2, U63_1, U71_3, U72_2, U73_2, U74_1, U81_2, U82_2, U83_1, U91_2, U92_1, proper_1, isPalListKind_1, isNeList_1, isList_1, isQid_1, isPal_1, isNePal_1, top_1 52.81/14.28 52.81/14.28 Defined Pair Symbols: __'_2, U11'_2, U12'_2, U13'_1, U21'_3, U22'_3, U23'_3, U24'_3, U25'_2, U26'_1, U31'_2, U32'_2, U33'_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_3, U72'_2, U73'_2, U74'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_1, ISPALLISTKIND_1, ISNELIST_1, ISLIST_1, ISQID_1, ISPAL_1, ISNEPAL_1, TOP_1 52.81/14.28 52.81/14.28 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_2 52.81/14.28 52.81/14.28 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (9) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) 52.81/14.28 Removed 1 trailing tuple parts 52.81/14.28 ---------------------------------------- 52.81/14.28 52.81/14.28 (10) 52.81/14.28 Obligation: 52.81/14.28 Complexity Dependency Tuples Problem 52.81/14.28 52.81/14.28 Rules: 52.81/14.28 __(mark(z0), z1) -> mark(__(z0, z1)) 52.81/14.28 __(z0, mark(z1)) -> mark(__(z0, z1)) 52.81/14.28 __(ok(z0), ok(z1)) -> ok(__(z0, z1)) 52.81/14.28 U11(mark(z0), z1) -> mark(U11(z0, z1)) 52.81/14.28 U11(ok(z0), ok(z1)) -> ok(U11(z0, z1)) 52.81/14.28 U12(mark(z0), z1) -> mark(U12(z0, z1)) 52.81/14.28 U12(ok(z0), ok(z1)) -> ok(U12(z0, z1)) 52.81/14.28 U13(mark(z0)) -> mark(U13(z0)) 52.81/14.28 U13(ok(z0)) -> ok(U13(z0)) 52.81/14.28 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 52.81/14.28 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 52.81/14.28 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 52.81/14.28 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 52.81/14.28 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 52.81/14.28 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 52.81/14.28 U24(mark(z0), z1, z2) -> mark(U24(z0, z1, z2)) 52.81/14.28 U24(ok(z0), ok(z1), ok(z2)) -> ok(U24(z0, z1, z2)) 52.81/14.28 U25(mark(z0), z1) -> mark(U25(z0, z1)) 52.81/14.28 U25(ok(z0), ok(z1)) -> ok(U25(z0, z1)) 52.81/14.28 U26(mark(z0)) -> mark(U26(z0)) 52.81/14.28 U26(ok(z0)) -> ok(U26(z0)) 52.81/14.28 U31(mark(z0), z1) -> mark(U31(z0, z1)) 52.81/14.28 U31(ok(z0), ok(z1)) -> ok(U31(z0, z1)) 52.81/14.28 U32(mark(z0), z1) -> mark(U32(z0, z1)) 52.81/14.28 U32(ok(z0), ok(z1)) -> ok(U32(z0, z1)) 52.81/14.28 U33(mark(z0)) -> mark(U33(z0)) 52.81/14.28 U33(ok(z0)) -> ok(U33(z0)) 52.81/14.28 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 52.81/14.28 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 52.81/14.28 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 52.81/14.28 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 52.81/14.28 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 52.81/14.28 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 52.81/14.28 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 52.81/14.28 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 52.81/14.28 U45(mark(z0), z1) -> mark(U45(z0, z1)) 52.81/14.28 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 52.81/14.28 U46(mark(z0)) -> mark(U46(z0)) 52.81/14.28 U46(ok(z0)) -> ok(U46(z0)) 52.81/14.28 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 52.81/14.28 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 52.81/14.28 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 52.81/14.28 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 52.81/14.28 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 52.81/14.28 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 52.81/14.28 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 52.81/14.28 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 52.81/14.29 U55(mark(z0), z1) -> mark(U55(z0, z1)) 52.81/14.29 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 52.81/14.29 U56(mark(z0)) -> mark(U56(z0)) 52.81/14.29 U56(ok(z0)) -> ok(U56(z0)) 52.81/14.29 U61(mark(z0), z1) -> mark(U61(z0, z1)) 52.81/14.29 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 52.81/14.29 U62(mark(z0), z1) -> mark(U62(z0, z1)) 52.81/14.29 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 52.81/14.29 U63(mark(z0)) -> mark(U63(z0)) 52.81/14.29 U63(ok(z0)) -> ok(U63(z0)) 52.81/14.29 U71(mark(z0), z1, z2) -> mark(U71(z0, z1, z2)) 52.81/14.29 U71(ok(z0), ok(z1), ok(z2)) -> ok(U71(z0, z1, z2)) 52.81/14.29 U72(mark(z0), z1) -> mark(U72(z0, z1)) 52.81/14.29 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 52.81/14.29 U73(mark(z0), z1) -> mark(U73(z0, z1)) 52.81/14.29 U73(ok(z0), ok(z1)) -> ok(U73(z0, z1)) 52.81/14.29 U74(mark(z0)) -> mark(U74(z0)) 52.81/14.29 U74(ok(z0)) -> ok(U74(z0)) 52.81/14.29 U81(mark(z0), z1) -> mark(U81(z0, z1)) 52.81/14.29 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 52.81/14.29 U82(mark(z0), z1) -> mark(U82(z0, z1)) 52.81/14.29 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 52.81/14.29 U83(mark(z0)) -> mark(U83(z0)) 52.81/14.29 U83(ok(z0)) -> ok(U83(z0)) 52.81/14.29 U91(mark(z0), z1) -> mark(U91(z0, z1)) 52.81/14.29 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 52.81/14.29 U92(mark(z0)) -> mark(U92(z0)) 52.81/14.29 U92(ok(z0)) -> ok(U92(z0)) 52.81/14.29 proper(nil) -> ok(nil) 52.81/14.29 proper(tt) -> ok(tt) 52.81/14.29 proper(a) -> ok(a) 52.81/14.29 proper(e) -> ok(e) 52.81/14.29 proper(i) -> ok(i) 52.81/14.29 proper(o) -> ok(o) 52.81/14.29 proper(u) -> ok(u) 52.81/14.29 isPalListKind(ok(z0)) -> ok(isPalListKind(z0)) 52.81/14.29 isNeList(ok(z0)) -> ok(isNeList(z0)) 52.81/14.29 isList(ok(z0)) -> ok(isList(z0)) 52.81/14.29 isQid(ok(z0)) -> ok(isQid(z0)) 52.81/14.29 isPal(ok(z0)) -> ok(isPal(z0)) 52.81/14.29 isNePal(ok(z0)) -> ok(isNePal(z0)) 52.81/14.29 top(mark(z0)) -> top(proper(z0)) 52.81/14.29 top(ok(z0)) -> top(active(z0)) 52.81/14.29 Tuples: 52.81/14.29 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.29 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.29 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.29 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.29 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.29 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.29 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.29 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.29 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.29 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.29 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.29 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.29 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.29 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.29 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.29 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.29 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.29 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.29 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.29 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.29 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.29 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.29 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.29 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.29 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.29 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.29 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.29 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.29 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.29 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.29 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.29 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.29 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.29 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.29 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.29 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.29 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.29 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.29 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.29 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.29 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.29 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.29 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.29 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.29 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.29 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.29 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.29 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.29 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.29 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.29 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.29 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.29 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.29 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.29 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.29 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.29 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.29 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.29 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.29 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.29 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.29 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.29 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.29 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.29 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.29 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.29 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.29 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.29 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.29 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.29 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.29 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.29 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.29 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.29 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.29 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.29 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.29 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.29 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.29 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.29 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.29 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.29 S tuples: 52.81/14.29 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.29 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.29 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.29 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.29 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.29 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.29 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.29 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.29 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.29 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.29 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.29 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.29 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.29 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.29 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.29 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.29 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.29 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.29 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.29 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.29 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.29 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.29 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.29 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.29 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.29 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.29 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.29 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.29 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.29 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.29 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.29 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.29 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.29 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.29 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.29 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.29 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.29 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.29 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.29 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.29 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.29 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.29 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.29 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.29 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.29 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.29 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.29 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.29 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.29 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.29 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.29 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.29 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.29 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.29 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.29 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.29 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.29 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.29 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.29 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.29 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.29 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.29 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.29 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.29 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.29 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.29 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.29 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.29 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.29 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.29 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.29 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.29 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.29 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.29 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.29 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.29 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.29 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.29 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.29 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.29 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.29 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.29 K tuples:none 52.81/14.29 Defined Rule Symbols: ___2, U11_2, U12_2, U13_1, U21_3, U22_3, U23_3, U24_3, U25_2, U26_1, U31_2, U32_2, U33_1, U41_3, U42_3, U43_3, U44_3, U45_2, U46_1, U51_3, U52_3, U53_3, U54_3, U55_2, U56_1, U61_2, U62_2, U63_1, U71_3, U72_2, U73_2, U74_1, U81_2, U82_2, U83_1, U91_2, U92_1, proper_1, isPalListKind_1, isNeList_1, isList_1, isQid_1, isPal_1, isNePal_1, top_1 52.81/14.29 52.81/14.29 Defined Pair Symbols: __'_2, U11'_2, U12'_2, U13'_1, U21'_3, U22'_3, U23'_3, U24'_3, U25'_2, U26'_1, U31'_2, U32'_2, U33'_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_3, U72'_2, U73'_2, U74'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_1, ISPALLISTKIND_1, ISNELIST_1, ISLIST_1, ISQID_1, ISPAL_1, ISNEPAL_1, TOP_1 52.81/14.29 52.81/14.29 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1 52.81/14.29 52.81/14.29 52.81/14.29 ---------------------------------------- 52.81/14.29 52.81/14.29 (11) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) 52.81/14.29 The following rules are not usable and were removed: 52.81/14.29 __(mark(z0), z1) -> mark(__(z0, z1)) 52.81/14.29 __(z0, mark(z1)) -> mark(__(z0, z1)) 52.81/14.29 __(ok(z0), ok(z1)) -> ok(__(z0, z1)) 52.81/14.29 U11(mark(z0), z1) -> mark(U11(z0, z1)) 52.81/14.29 U11(ok(z0), ok(z1)) -> ok(U11(z0, z1)) 52.81/14.29 U12(mark(z0), z1) -> mark(U12(z0, z1)) 52.81/14.29 U12(ok(z0), ok(z1)) -> ok(U12(z0, z1)) 52.81/14.29 U13(mark(z0)) -> mark(U13(z0)) 52.81/14.29 U13(ok(z0)) -> ok(U13(z0)) 52.81/14.29 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 52.81/14.29 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 52.81/14.29 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 52.81/14.29 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 52.81/14.29 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 52.81/14.29 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 52.81/14.29 U24(mark(z0), z1, z2) -> mark(U24(z0, z1, z2)) 52.81/14.29 U24(ok(z0), ok(z1), ok(z2)) -> ok(U24(z0, z1, z2)) 52.81/14.29 U25(mark(z0), z1) -> mark(U25(z0, z1)) 52.81/14.29 U25(ok(z0), ok(z1)) -> ok(U25(z0, z1)) 52.81/14.29 U26(mark(z0)) -> mark(U26(z0)) 52.81/14.29 U26(ok(z0)) -> ok(U26(z0)) 52.81/14.29 U31(mark(z0), z1) -> mark(U31(z0, z1)) 52.81/14.29 U31(ok(z0), ok(z1)) -> ok(U31(z0, z1)) 52.81/14.29 U32(mark(z0), z1) -> mark(U32(z0, z1)) 52.81/14.29 U32(ok(z0), ok(z1)) -> ok(U32(z0, z1)) 52.81/14.29 U33(mark(z0)) -> mark(U33(z0)) 52.81/14.29 U33(ok(z0)) -> ok(U33(z0)) 52.81/14.29 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 52.81/14.29 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 52.81/14.29 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 52.81/14.29 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 52.81/14.29 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 52.81/14.29 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 52.81/14.29 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 52.81/14.29 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 52.81/14.29 U45(mark(z0), z1) -> mark(U45(z0, z1)) 52.81/14.29 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 52.81/14.29 U46(mark(z0)) -> mark(U46(z0)) 52.81/14.29 U46(ok(z0)) -> ok(U46(z0)) 52.81/14.29 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 52.81/14.29 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 52.81/14.29 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 52.81/14.29 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 52.81/14.29 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 52.81/14.29 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 52.81/14.29 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 52.81/14.29 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 52.81/14.29 U55(mark(z0), z1) -> mark(U55(z0, z1)) 52.81/14.29 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 52.81/14.29 U56(mark(z0)) -> mark(U56(z0)) 52.81/14.29 U56(ok(z0)) -> ok(U56(z0)) 52.81/14.29 U61(mark(z0), z1) -> mark(U61(z0, z1)) 52.81/14.29 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 52.81/14.29 U62(mark(z0), z1) -> mark(U62(z0, z1)) 52.81/14.29 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 52.81/14.29 U63(mark(z0)) -> mark(U63(z0)) 52.81/14.29 U63(ok(z0)) -> ok(U63(z0)) 52.81/14.29 U71(mark(z0), z1, z2) -> mark(U71(z0, z1, z2)) 52.81/14.29 U71(ok(z0), ok(z1), ok(z2)) -> ok(U71(z0, z1, z2)) 52.81/14.29 U72(mark(z0), z1) -> mark(U72(z0, z1)) 52.81/14.29 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 52.81/14.29 U73(mark(z0), z1) -> mark(U73(z0, z1)) 52.81/14.29 U73(ok(z0), ok(z1)) -> ok(U73(z0, z1)) 52.81/14.29 U74(mark(z0)) -> mark(U74(z0)) 52.81/14.29 U74(ok(z0)) -> ok(U74(z0)) 52.81/14.29 U81(mark(z0), z1) -> mark(U81(z0, z1)) 52.81/14.29 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 52.81/14.29 U82(mark(z0), z1) -> mark(U82(z0, z1)) 52.81/14.29 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 52.81/14.29 U83(mark(z0)) -> mark(U83(z0)) 52.81/14.29 U83(ok(z0)) -> ok(U83(z0)) 52.81/14.29 U91(mark(z0), z1) -> mark(U91(z0, z1)) 52.81/14.29 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 52.81/14.29 U92(mark(z0)) -> mark(U92(z0)) 52.81/14.29 U92(ok(z0)) -> ok(U92(z0)) 52.81/14.29 isPalListKind(ok(z0)) -> ok(isPalListKind(z0)) 52.81/14.29 isNeList(ok(z0)) -> ok(isNeList(z0)) 52.81/14.29 isList(ok(z0)) -> ok(isList(z0)) 52.81/14.29 isQid(ok(z0)) -> ok(isQid(z0)) 52.81/14.29 isPal(ok(z0)) -> ok(isPal(z0)) 52.81/14.29 isNePal(ok(z0)) -> ok(isNePal(z0)) 52.81/14.29 top(mark(z0)) -> top(proper(z0)) 52.81/14.29 top(ok(z0)) -> top(active(z0)) 52.81/14.29 52.81/14.29 ---------------------------------------- 52.81/14.29 52.81/14.29 (12) 52.81/14.29 Obligation: 52.81/14.29 Complexity Dependency Tuples Problem 52.81/14.29 52.81/14.29 Rules: 52.81/14.29 proper(nil) -> ok(nil) 52.81/14.29 proper(tt) -> ok(tt) 52.81/14.29 proper(a) -> ok(a) 52.81/14.29 proper(e) -> ok(e) 52.81/14.29 proper(i) -> ok(i) 52.81/14.29 proper(o) -> ok(o) 52.81/14.29 proper(u) -> ok(u) 52.81/14.29 Tuples: 52.81/14.29 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.29 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.29 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.29 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.29 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.29 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.29 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.29 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.29 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.29 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.29 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.29 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.29 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.29 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.29 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.29 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.29 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.29 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.29 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.29 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.29 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.29 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.29 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.29 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.29 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.29 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.29 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.29 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.29 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.29 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.29 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.29 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.29 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.29 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.29 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.29 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.29 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.29 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.29 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.29 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.29 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.29 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.29 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.29 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.29 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.29 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.29 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.29 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.29 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.29 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.29 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.29 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.29 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.29 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.29 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.29 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.29 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.29 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.29 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.29 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.29 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.29 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.29 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.29 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.29 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.29 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.29 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.29 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.29 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.29 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.29 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.29 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.29 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.29 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.29 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.29 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.29 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.29 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.29 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.29 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.29 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.29 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.29 S tuples: 52.81/14.29 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.29 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.29 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.29 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.29 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.29 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.29 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.29 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.29 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.29 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.29 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.29 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.29 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.29 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.29 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.29 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.29 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.29 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.29 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.29 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.29 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.29 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.29 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.29 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.29 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.29 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.29 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.29 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.29 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.29 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.29 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.29 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.29 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.29 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.29 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.29 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.29 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.29 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.29 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.29 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.29 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.29 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.29 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.29 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.29 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.29 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.29 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.29 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.29 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.29 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.29 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.29 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.29 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.29 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.29 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.29 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.29 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.29 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.29 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.29 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.29 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.29 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.29 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.29 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.29 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.29 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.29 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.29 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.29 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.29 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.29 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.29 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.29 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.29 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.29 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.29 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.29 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.29 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.29 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.29 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.29 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.29 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.29 K tuples:none 52.81/14.29 Defined Rule Symbols: proper_1 52.81/14.29 52.81/14.29 Defined Pair Symbols: __'_2, U11'_2, U12'_2, U13'_1, U21'_3, U22'_3, U23'_3, U24'_3, U25'_2, U26'_1, U31'_2, U32'_2, U33'_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_3, U72'_2, U73'_2, U74'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_1, ISPALLISTKIND_1, ISNELIST_1, ISLIST_1, ISQID_1, ISPAL_1, ISNEPAL_1, TOP_1 52.81/14.29 52.81/14.29 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1 52.81/14.29 52.81/14.29 52.81/14.29 ---------------------------------------- 52.81/14.30 52.81/14.30 (13) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 52.81/14.30 Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 We considered the (Usable) Rules: 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 And the Tuples: 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 The order we found is given by the following interpretation: 52.81/14.30 52.81/14.30 Polynomial interpretation : 52.81/14.30 52.81/14.30 POL(ISLIST(x_1)) = x_1 52.81/14.30 POL(ISNELIST(x_1)) = x_1 52.81/14.30 POL(ISNEPAL(x_1)) = x_1 52.81/14.30 POL(ISPAL(x_1)) = x_1 52.81/14.30 POL(ISPALLISTKIND(x_1)) = x_1 52.81/14.30 POL(ISQID(x_1)) = x_1 52.81/14.30 POL(TOP(x_1)) = x_1 52.81/14.30 POL(U11'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U12'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U13'(x_1)) = x_1 52.81/14.30 POL(U21'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U22'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U23'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U24'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U25'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U26'(x_1)) = x_1 52.81/14.30 POL(U31'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U32'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U33'(x_1)) = x_1 52.81/14.30 POL(U41'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U42'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U43'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U44'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U45'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U46'(x_1)) = x_1 52.81/14.30 POL(U51'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U52'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U53'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U54'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U55'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U56'(x_1)) = x_1 52.81/14.30 POL(U61'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U62'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U63'(x_1)) = x_1 52.81/14.30 POL(U71'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U72'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U73'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U74'(x_1)) = x_1 52.81/14.30 POL(U81'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U82'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U83'(x_1)) = x_1 52.81/14.30 POL(U91'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U92'(x_1)) = x_1 52.81/14.30 POL(__'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(a) = [1] 52.81/14.30 POL(c(x_1)) = x_1 52.81/14.30 POL(c1(x_1)) = x_1 52.81/14.30 POL(c10(x_1)) = x_1 52.81/14.30 POL(c11(x_1)) = x_1 52.81/14.30 POL(c12(x_1)) = x_1 52.81/14.30 POL(c13(x_1)) = x_1 52.81/14.30 POL(c14(x_1)) = x_1 52.81/14.30 POL(c15(x_1)) = x_1 52.81/14.30 POL(c16(x_1)) = x_1 52.81/14.30 POL(c17(x_1)) = x_1 52.81/14.30 POL(c18(x_1)) = x_1 52.81/14.30 POL(c19(x_1)) = x_1 52.81/14.30 POL(c2(x_1)) = x_1 52.81/14.30 POL(c20(x_1)) = x_1 52.81/14.30 POL(c21(x_1)) = x_1 52.81/14.30 POL(c22(x_1)) = x_1 52.81/14.30 POL(c23(x_1)) = x_1 52.81/14.30 POL(c24(x_1)) = x_1 52.81/14.30 POL(c25(x_1)) = x_1 52.81/14.30 POL(c26(x_1)) = x_1 52.81/14.30 POL(c27(x_1)) = x_1 52.81/14.30 POL(c28(x_1)) = x_1 52.81/14.30 POL(c29(x_1)) = x_1 52.81/14.30 POL(c3(x_1)) = x_1 52.81/14.30 POL(c30(x_1)) = x_1 52.81/14.30 POL(c31(x_1)) = x_1 52.81/14.30 POL(c32(x_1)) = x_1 52.81/14.30 POL(c33(x_1)) = x_1 52.81/14.30 POL(c34(x_1)) = x_1 52.81/14.30 POL(c35(x_1)) = x_1 52.81/14.30 POL(c36(x_1)) = x_1 52.81/14.30 POL(c37(x_1)) = x_1 52.81/14.30 POL(c38(x_1)) = x_1 52.81/14.30 POL(c39(x_1)) = x_1 52.81/14.30 POL(c4(x_1)) = x_1 52.81/14.30 POL(c40(x_1)) = x_1 52.81/14.30 POL(c41(x_1)) = x_1 52.81/14.30 POL(c42(x_1)) = x_1 52.81/14.30 POL(c43(x_1)) = x_1 52.81/14.30 POL(c44(x_1)) = x_1 52.81/14.30 POL(c45(x_1)) = x_1 52.81/14.30 POL(c46(x_1)) = x_1 52.81/14.30 POL(c47(x_1)) = x_1 52.81/14.30 POL(c48(x_1)) = x_1 52.81/14.30 POL(c49(x_1)) = x_1 52.81/14.30 POL(c5(x_1)) = x_1 52.81/14.30 POL(c50(x_1)) = x_1 52.81/14.30 POL(c51(x_1)) = x_1 52.81/14.30 POL(c52(x_1)) = x_1 52.81/14.30 POL(c53(x_1)) = x_1 52.81/14.30 POL(c54(x_1)) = x_1 52.81/14.30 POL(c55(x_1)) = x_1 52.81/14.30 POL(c56(x_1)) = x_1 52.81/14.30 POL(c57(x_1)) = x_1 52.81/14.30 POL(c58(x_1)) = x_1 52.81/14.30 POL(c59(x_1)) = x_1 52.81/14.30 POL(c6(x_1)) = x_1 52.81/14.30 POL(c60(x_1)) = x_1 52.81/14.30 POL(c61(x_1)) = x_1 52.81/14.30 POL(c62(x_1)) = x_1 52.81/14.30 POL(c63(x_1)) = x_1 52.81/14.30 POL(c64(x_1)) = x_1 52.81/14.30 POL(c65(x_1)) = x_1 52.81/14.30 POL(c66(x_1)) = x_1 52.81/14.30 POL(c67(x_1)) = x_1 52.81/14.30 POL(c68(x_1)) = x_1 52.81/14.30 POL(c69(x_1)) = x_1 52.81/14.30 POL(c7(x_1)) = x_1 52.81/14.30 POL(c70(x_1)) = x_1 52.81/14.30 POL(c71(x_1)) = x_1 52.81/14.30 POL(c72(x_1)) = x_1 52.81/14.30 POL(c73(x_1)) = x_1 52.81/14.30 POL(c74(x_1)) = x_1 52.81/14.30 POL(c8(x_1)) = x_1 52.81/14.30 POL(c82(x_1)) = x_1 52.81/14.30 POL(c83(x_1)) = x_1 52.81/14.30 POL(c84(x_1)) = x_1 52.81/14.30 POL(c85(x_1)) = x_1 52.81/14.30 POL(c86(x_1)) = x_1 52.81/14.30 POL(c87(x_1)) = x_1 52.81/14.30 POL(c88(x_1)) = x_1 52.81/14.30 POL(c9(x_1)) = x_1 52.81/14.30 POL(e) = [1] 52.81/14.30 POL(i) = [1] 52.81/14.30 POL(mark(x_1)) = [1] + x_1 52.81/14.30 POL(nil) = [1] 52.81/14.30 POL(o) = [1] 52.81/14.30 POL(ok(x_1)) = [1] + x_1 52.81/14.30 POL(proper(x_1)) = [1] + x_1 52.81/14.30 POL(tt) = [1] 52.81/14.30 POL(u) = [1] 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (14) 52.81/14.30 Obligation: 52.81/14.30 Complexity Dependency Tuples Problem 52.81/14.30 52.81/14.30 Rules: 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 Tuples: 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 S tuples: 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 K tuples: 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 Defined Rule Symbols: proper_1 52.81/14.30 52.81/14.30 Defined Pair Symbols: __'_2, U11'_2, U12'_2, U13'_1, U21'_3, U22'_3, U23'_3, U24'_3, U25'_2, U26'_1, U31'_2, U32'_2, U33'_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_3, U72'_2, U73'_2, U74'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_1, ISPALLISTKIND_1, ISNELIST_1, ISLIST_1, ISQID_1, ISPAL_1, ISNEPAL_1, TOP_1 52.81/14.30 52.81/14.30 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1 52.81/14.30 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (15) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 52.81/14.30 Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 We considered the (Usable) Rules: 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 And the Tuples: 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 The order we found is given by the following interpretation: 52.81/14.30 52.81/14.30 Polynomial interpretation : 52.81/14.30 52.81/14.30 POL(ISLIST(x_1)) = x_1 52.81/14.30 POL(ISNELIST(x_1)) = x_1 52.81/14.30 POL(ISNEPAL(x_1)) = x_1 52.81/14.30 POL(ISPAL(x_1)) = x_1 52.81/14.30 POL(ISPALLISTKIND(x_1)) = x_1 52.81/14.30 POL(ISQID(x_1)) = x_1 52.81/14.30 POL(TOP(x_1)) = x_1 52.81/14.30 POL(U11'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U12'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U13'(x_1)) = x_1 52.81/14.30 POL(U21'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U22'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U23'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U24'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U25'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U26'(x_1)) = x_1 52.81/14.30 POL(U31'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U32'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U33'(x_1)) = x_1 52.81/14.30 POL(U41'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U42'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U43'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U44'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U45'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U46'(x_1)) = x_1 52.81/14.30 POL(U51'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U52'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U53'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U54'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U55'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U56'(x_1)) = x_1 52.81/14.30 POL(U61'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U62'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U63'(x_1)) = x_1 52.81/14.30 POL(U71'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 52.81/14.30 POL(U72'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U73'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U74'(x_1)) = x_1 52.81/14.30 POL(U81'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U82'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U83'(x_1)) = x_1 52.81/14.30 POL(U91'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(U92'(x_1)) = x_1 52.81/14.30 POL(__'(x_1, x_2)) = x_1 + x_2 52.81/14.30 POL(a) = [1] 52.81/14.30 POL(c(x_1)) = x_1 52.81/14.30 POL(c1(x_1)) = x_1 52.81/14.30 POL(c10(x_1)) = x_1 52.81/14.30 POL(c11(x_1)) = x_1 52.81/14.30 POL(c12(x_1)) = x_1 52.81/14.30 POL(c13(x_1)) = x_1 52.81/14.30 POL(c14(x_1)) = x_1 52.81/14.30 POL(c15(x_1)) = x_1 52.81/14.30 POL(c16(x_1)) = x_1 52.81/14.30 POL(c17(x_1)) = x_1 52.81/14.30 POL(c18(x_1)) = x_1 52.81/14.30 POL(c19(x_1)) = x_1 52.81/14.30 POL(c2(x_1)) = x_1 52.81/14.30 POL(c20(x_1)) = x_1 52.81/14.30 POL(c21(x_1)) = x_1 52.81/14.30 POL(c22(x_1)) = x_1 52.81/14.30 POL(c23(x_1)) = x_1 52.81/14.30 POL(c24(x_1)) = x_1 52.81/14.30 POL(c25(x_1)) = x_1 52.81/14.30 POL(c26(x_1)) = x_1 52.81/14.30 POL(c27(x_1)) = x_1 52.81/14.30 POL(c28(x_1)) = x_1 52.81/14.30 POL(c29(x_1)) = x_1 52.81/14.30 POL(c3(x_1)) = x_1 52.81/14.30 POL(c30(x_1)) = x_1 52.81/14.30 POL(c31(x_1)) = x_1 52.81/14.30 POL(c32(x_1)) = x_1 52.81/14.30 POL(c33(x_1)) = x_1 52.81/14.30 POL(c34(x_1)) = x_1 52.81/14.30 POL(c35(x_1)) = x_1 52.81/14.30 POL(c36(x_1)) = x_1 52.81/14.30 POL(c37(x_1)) = x_1 52.81/14.30 POL(c38(x_1)) = x_1 52.81/14.30 POL(c39(x_1)) = x_1 52.81/14.30 POL(c4(x_1)) = x_1 52.81/14.30 POL(c40(x_1)) = x_1 52.81/14.30 POL(c41(x_1)) = x_1 52.81/14.30 POL(c42(x_1)) = x_1 52.81/14.30 POL(c43(x_1)) = x_1 52.81/14.30 POL(c44(x_1)) = x_1 52.81/14.30 POL(c45(x_1)) = x_1 52.81/14.30 POL(c46(x_1)) = x_1 52.81/14.30 POL(c47(x_1)) = x_1 52.81/14.30 POL(c48(x_1)) = x_1 52.81/14.30 POL(c49(x_1)) = x_1 52.81/14.30 POL(c5(x_1)) = x_1 52.81/14.30 POL(c50(x_1)) = x_1 52.81/14.30 POL(c51(x_1)) = x_1 52.81/14.30 POL(c52(x_1)) = x_1 52.81/14.30 POL(c53(x_1)) = x_1 52.81/14.30 POL(c54(x_1)) = x_1 52.81/14.30 POL(c55(x_1)) = x_1 52.81/14.30 POL(c56(x_1)) = x_1 52.81/14.30 POL(c57(x_1)) = x_1 52.81/14.30 POL(c58(x_1)) = x_1 52.81/14.30 POL(c59(x_1)) = x_1 52.81/14.30 POL(c6(x_1)) = x_1 52.81/14.30 POL(c60(x_1)) = x_1 52.81/14.30 POL(c61(x_1)) = x_1 52.81/14.30 POL(c62(x_1)) = x_1 52.81/14.30 POL(c63(x_1)) = x_1 52.81/14.30 POL(c64(x_1)) = x_1 52.81/14.30 POL(c65(x_1)) = x_1 52.81/14.30 POL(c66(x_1)) = x_1 52.81/14.30 POL(c67(x_1)) = x_1 52.81/14.30 POL(c68(x_1)) = x_1 52.81/14.30 POL(c69(x_1)) = x_1 52.81/14.30 POL(c7(x_1)) = x_1 52.81/14.30 POL(c70(x_1)) = x_1 52.81/14.30 POL(c71(x_1)) = x_1 52.81/14.30 POL(c72(x_1)) = x_1 52.81/14.30 POL(c73(x_1)) = x_1 52.81/14.30 POL(c74(x_1)) = x_1 52.81/14.30 POL(c8(x_1)) = x_1 52.81/14.30 POL(c82(x_1)) = x_1 52.81/14.30 POL(c83(x_1)) = x_1 52.81/14.30 POL(c84(x_1)) = x_1 52.81/14.30 POL(c85(x_1)) = x_1 52.81/14.30 POL(c86(x_1)) = x_1 52.81/14.30 POL(c87(x_1)) = x_1 52.81/14.30 POL(c88(x_1)) = x_1 52.81/14.30 POL(c9(x_1)) = x_1 52.81/14.30 POL(e) = [1] 52.81/14.30 POL(i) = [1] 52.81/14.30 POL(mark(x_1)) = [1] + x_1 52.81/14.30 POL(nil) = [1] 52.81/14.30 POL(o) = [1] 52.81/14.30 POL(ok(x_1)) = x_1 52.81/14.30 POL(proper(x_1)) = x_1 52.81/14.30 POL(tt) = [1] 52.81/14.30 POL(u) = [1] 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (16) 52.81/14.30 Obligation: 52.81/14.30 Complexity Dependency Tuples Problem 52.81/14.30 52.81/14.30 Rules: 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 Tuples: 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 S tuples:none 52.81/14.30 K tuples: 52.81/14.30 __'(mark(z0), z1) -> c(__'(z0, z1)) 52.81/14.30 __'(z0, mark(z1)) -> c1(__'(z0, z1)) 52.81/14.30 __'(ok(z0), ok(z1)) -> c2(__'(z0, z1)) 52.81/14.30 U11'(mark(z0), z1) -> c3(U11'(z0, z1)) 52.81/14.30 U11'(ok(z0), ok(z1)) -> c4(U11'(z0, z1)) 52.81/14.30 U12'(mark(z0), z1) -> c5(U12'(z0, z1)) 52.81/14.30 U12'(ok(z0), ok(z1)) -> c6(U12'(z0, z1)) 52.81/14.30 U13'(mark(z0)) -> c7(U13'(z0)) 52.81/14.30 U13'(ok(z0)) -> c8(U13'(z0)) 52.81/14.30 U21'(mark(z0), z1, z2) -> c9(U21'(z0, z1, z2)) 52.81/14.30 U21'(ok(z0), ok(z1), ok(z2)) -> c10(U21'(z0, z1, z2)) 52.81/14.30 U22'(mark(z0), z1, z2) -> c11(U22'(z0, z1, z2)) 52.81/14.30 U22'(ok(z0), ok(z1), ok(z2)) -> c12(U22'(z0, z1, z2)) 52.81/14.30 U23'(mark(z0), z1, z2) -> c13(U23'(z0, z1, z2)) 52.81/14.30 U23'(ok(z0), ok(z1), ok(z2)) -> c14(U23'(z0, z1, z2)) 52.81/14.30 U24'(mark(z0), z1, z2) -> c15(U24'(z0, z1, z2)) 52.81/14.30 U24'(ok(z0), ok(z1), ok(z2)) -> c16(U24'(z0, z1, z2)) 52.81/14.30 U25'(mark(z0), z1) -> c17(U25'(z0, z1)) 52.81/14.30 U25'(ok(z0), ok(z1)) -> c18(U25'(z0, z1)) 52.81/14.30 U26'(mark(z0)) -> c19(U26'(z0)) 52.81/14.30 U26'(ok(z0)) -> c20(U26'(z0)) 52.81/14.30 U31'(mark(z0), z1) -> c21(U31'(z0, z1)) 52.81/14.30 U31'(ok(z0), ok(z1)) -> c22(U31'(z0, z1)) 52.81/14.30 U32'(mark(z0), z1) -> c23(U32'(z0, z1)) 52.81/14.30 U32'(ok(z0), ok(z1)) -> c24(U32'(z0, z1)) 52.81/14.30 U33'(mark(z0)) -> c25(U33'(z0)) 52.81/14.30 U33'(ok(z0)) -> c26(U33'(z0)) 52.81/14.30 U41'(mark(z0), z1, z2) -> c27(U41'(z0, z1, z2)) 52.81/14.30 U41'(ok(z0), ok(z1), ok(z2)) -> c28(U41'(z0, z1, z2)) 52.81/14.30 U42'(mark(z0), z1, z2) -> c29(U42'(z0, z1, z2)) 52.81/14.30 U42'(ok(z0), ok(z1), ok(z2)) -> c30(U42'(z0, z1, z2)) 52.81/14.30 U43'(mark(z0), z1, z2) -> c31(U43'(z0, z1, z2)) 52.81/14.30 U43'(ok(z0), ok(z1), ok(z2)) -> c32(U43'(z0, z1, z2)) 52.81/14.30 U44'(mark(z0), z1, z2) -> c33(U44'(z0, z1, z2)) 52.81/14.30 U44'(ok(z0), ok(z1), ok(z2)) -> c34(U44'(z0, z1, z2)) 52.81/14.30 U45'(mark(z0), z1) -> c35(U45'(z0, z1)) 52.81/14.30 U45'(ok(z0), ok(z1)) -> c36(U45'(z0, z1)) 52.81/14.30 U46'(mark(z0)) -> c37(U46'(z0)) 52.81/14.30 U46'(ok(z0)) -> c38(U46'(z0)) 52.81/14.30 U51'(mark(z0), z1, z2) -> c39(U51'(z0, z1, z2)) 52.81/14.30 U51'(ok(z0), ok(z1), ok(z2)) -> c40(U51'(z0, z1, z2)) 52.81/14.30 U52'(mark(z0), z1, z2) -> c41(U52'(z0, z1, z2)) 52.81/14.30 U52'(ok(z0), ok(z1), ok(z2)) -> c42(U52'(z0, z1, z2)) 52.81/14.30 U53'(mark(z0), z1, z2) -> c43(U53'(z0, z1, z2)) 52.81/14.30 U53'(ok(z0), ok(z1), ok(z2)) -> c44(U53'(z0, z1, z2)) 52.81/14.30 U54'(mark(z0), z1, z2) -> c45(U54'(z0, z1, z2)) 52.81/14.30 U54'(ok(z0), ok(z1), ok(z2)) -> c46(U54'(z0, z1, z2)) 52.81/14.30 U55'(mark(z0), z1) -> c47(U55'(z0, z1)) 52.81/14.30 U55'(ok(z0), ok(z1)) -> c48(U55'(z0, z1)) 52.81/14.30 U56'(mark(z0)) -> c49(U56'(z0)) 52.81/14.30 U56'(ok(z0)) -> c50(U56'(z0)) 52.81/14.30 U61'(mark(z0), z1) -> c51(U61'(z0, z1)) 52.81/14.30 U61'(ok(z0), ok(z1)) -> c52(U61'(z0, z1)) 52.81/14.30 U62'(mark(z0), z1) -> c53(U62'(z0, z1)) 52.81/14.30 U62'(ok(z0), ok(z1)) -> c54(U62'(z0, z1)) 52.81/14.30 U63'(mark(z0)) -> c55(U63'(z0)) 52.81/14.30 U63'(ok(z0)) -> c56(U63'(z0)) 52.81/14.30 U71'(mark(z0), z1, z2) -> c57(U71'(z0, z1, z2)) 52.81/14.30 U71'(ok(z0), ok(z1), ok(z2)) -> c58(U71'(z0, z1, z2)) 52.81/14.30 U72'(mark(z0), z1) -> c59(U72'(z0, z1)) 52.81/14.30 U72'(ok(z0), ok(z1)) -> c60(U72'(z0, z1)) 52.81/14.30 U73'(mark(z0), z1) -> c61(U73'(z0, z1)) 52.81/14.30 U73'(ok(z0), ok(z1)) -> c62(U73'(z0, z1)) 52.81/14.30 U74'(mark(z0)) -> c63(U74'(z0)) 52.81/14.30 U74'(ok(z0)) -> c64(U74'(z0)) 52.81/14.30 U81'(mark(z0), z1) -> c65(U81'(z0, z1)) 52.81/14.30 U81'(ok(z0), ok(z1)) -> c66(U81'(z0, z1)) 52.81/14.30 U82'(mark(z0), z1) -> c67(U82'(z0, z1)) 52.81/14.30 U82'(ok(z0), ok(z1)) -> c68(U82'(z0, z1)) 52.81/14.30 U83'(mark(z0)) -> c69(U83'(z0)) 52.81/14.30 U83'(ok(z0)) -> c70(U83'(z0)) 52.81/14.30 U91'(mark(z0), z1) -> c71(U91'(z0, z1)) 52.81/14.30 U91'(ok(z0), ok(z1)) -> c72(U91'(z0, z1)) 52.81/14.30 U92'(mark(z0)) -> c73(U92'(z0)) 52.81/14.30 U92'(ok(z0)) -> c74(U92'(z0)) 52.81/14.30 ISPALLISTKIND(ok(z0)) -> c82(ISPALLISTKIND(z0)) 52.81/14.30 ISNELIST(ok(z0)) -> c83(ISNELIST(z0)) 52.81/14.30 ISLIST(ok(z0)) -> c84(ISLIST(z0)) 52.81/14.30 ISQID(ok(z0)) -> c85(ISQID(z0)) 52.81/14.30 ISPAL(ok(z0)) -> c86(ISPAL(z0)) 52.81/14.30 ISNEPAL(ok(z0)) -> c87(ISNEPAL(z0)) 52.81/14.30 TOP(mark(z0)) -> c88(TOP(proper(z0))) 52.81/14.30 Defined Rule Symbols: proper_1 52.81/14.30 52.81/14.30 Defined Pair Symbols: __'_2, U11'_2, U12'_2, U13'_1, U21'_3, U22'_3, U23'_3, U24'_3, U25'_2, U26'_1, U31'_2, U32'_2, U33'_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_3, U72'_2, U73'_2, U74'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_1, ISPALLISTKIND_1, ISNELIST_1, ISLIST_1, ISQID_1, ISPAL_1, ISNEPAL_1, TOP_1 52.81/14.30 52.81/14.30 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1 52.81/14.30 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (17) SIsEmptyProof (BOTH BOUNDS(ID, ID)) 52.81/14.30 The set S is empty 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (18) 52.81/14.30 BOUNDS(1, 1) 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (19) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 52.81/14.30 Transformed a relative TRS into a decreasing-loop problem. 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (20) 52.81/14.30 Obligation: 52.81/14.30 Analyzing the following TRS for decreasing loops: 52.81/14.30 52.81/14.30 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 52.81/14.30 52.81/14.30 52.81/14.30 The TRS R consists of the following rules: 52.81/14.30 52.81/14.30 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 52.81/14.30 active(__(X, nil)) -> mark(X) 52.81/14.30 active(__(nil, X)) -> mark(X) 52.81/14.30 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 52.81/14.30 active(U12(tt, V)) -> mark(U13(isNeList(V))) 52.81/14.30 active(U13(tt)) -> mark(tt) 52.81/14.30 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 52.81/14.30 active(U25(tt, V2)) -> mark(U26(isList(V2))) 52.81/14.30 active(U26(tt)) -> mark(tt) 52.81/14.30 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 52.81/14.30 active(U32(tt, V)) -> mark(U33(isQid(V))) 52.81/14.30 active(U33(tt)) -> mark(tt) 52.81/14.30 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 52.81/14.30 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 52.81/14.30 active(U46(tt)) -> mark(tt) 52.81/14.30 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 52.81/14.30 active(U55(tt, V2)) -> mark(U56(isList(V2))) 52.81/14.30 active(U56(tt)) -> mark(tt) 52.81/14.30 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 52.81/14.30 active(U62(tt, V)) -> mark(U63(isQid(V))) 52.81/14.30 active(U63(tt)) -> mark(tt) 52.81/14.30 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 52.81/14.30 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 52.81/14.30 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 52.81/14.30 active(U74(tt)) -> mark(tt) 52.81/14.30 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 52.81/14.30 active(U82(tt, V)) -> mark(U83(isNePal(V))) 52.81/14.30 active(U83(tt)) -> mark(tt) 52.81/14.30 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 52.81/14.30 active(U92(tt)) -> mark(tt) 52.81/14.30 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 52.81/14.30 active(isList(nil)) -> mark(tt) 52.81/14.30 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 52.81/14.30 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 52.81/14.30 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 52.81/14.30 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 52.81/14.30 active(isPal(nil)) -> mark(tt) 52.81/14.30 active(isPalListKind(a)) -> mark(tt) 52.81/14.30 active(isPalListKind(e)) -> mark(tt) 52.81/14.30 active(isPalListKind(i)) -> mark(tt) 52.81/14.30 active(isPalListKind(nil)) -> mark(tt) 52.81/14.30 active(isPalListKind(o)) -> mark(tt) 52.81/14.30 active(isPalListKind(u)) -> mark(tt) 52.81/14.30 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 52.81/14.30 active(isQid(a)) -> mark(tt) 52.81/14.30 active(isQid(e)) -> mark(tt) 52.81/14.30 active(isQid(i)) -> mark(tt) 52.81/14.30 active(isQid(o)) -> mark(tt) 52.81/14.30 active(isQid(u)) -> mark(tt) 52.81/14.30 active(__(X1, X2)) -> __(active(X1), X2) 52.81/14.30 active(__(X1, X2)) -> __(X1, active(X2)) 52.81/14.30 active(U11(X1, X2)) -> U11(active(X1), X2) 52.81/14.30 active(U12(X1, X2)) -> U12(active(X1), X2) 52.81/14.30 active(U13(X)) -> U13(active(X)) 52.81/14.30 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 52.81/14.30 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 52.81/14.30 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 52.81/14.30 active(U24(X1, X2, X3)) -> U24(active(X1), X2, X3) 52.81/14.30 active(U25(X1, X2)) -> U25(active(X1), X2) 52.81/14.30 active(U26(X)) -> U26(active(X)) 52.81/14.30 active(U31(X1, X2)) -> U31(active(X1), X2) 52.81/14.30 active(U32(X1, X2)) -> U32(active(X1), X2) 52.81/14.30 active(U33(X)) -> U33(active(X)) 52.81/14.30 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 52.81/14.30 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 52.81/14.30 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 52.81/14.30 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 52.81/14.30 active(U45(X1, X2)) -> U45(active(X1), X2) 52.81/14.30 active(U46(X)) -> U46(active(X)) 52.81/14.30 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 52.81/14.30 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 52.81/14.30 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 52.81/14.30 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 52.81/14.30 active(U55(X1, X2)) -> U55(active(X1), X2) 52.81/14.30 active(U56(X)) -> U56(active(X)) 52.81/14.30 active(U61(X1, X2)) -> U61(active(X1), X2) 52.81/14.30 active(U62(X1, X2)) -> U62(active(X1), X2) 52.81/14.30 active(U63(X)) -> U63(active(X)) 52.81/14.30 active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) 52.81/14.30 active(U72(X1, X2)) -> U72(active(X1), X2) 52.81/14.30 active(U73(X1, X2)) -> U73(active(X1), X2) 52.81/14.30 active(U74(X)) -> U74(active(X)) 52.81/14.30 active(U81(X1, X2)) -> U81(active(X1), X2) 52.81/14.30 active(U82(X1, X2)) -> U82(active(X1), X2) 52.81/14.30 active(U83(X)) -> U83(active(X)) 52.81/14.30 active(U91(X1, X2)) -> U91(active(X1), X2) 52.81/14.30 active(U92(X)) -> U92(active(X)) 52.81/14.30 __(mark(X1), X2) -> mark(__(X1, X2)) 52.81/14.30 __(X1, mark(X2)) -> mark(__(X1, X2)) 52.81/14.30 U11(mark(X1), X2) -> mark(U11(X1, X2)) 52.81/14.30 U12(mark(X1), X2) -> mark(U12(X1, X2)) 52.81/14.30 U13(mark(X)) -> mark(U13(X)) 52.81/14.30 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 52.81/14.30 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 52.81/14.30 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 52.81/14.30 U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3)) 52.81/14.30 U25(mark(X1), X2) -> mark(U25(X1, X2)) 52.81/14.30 U26(mark(X)) -> mark(U26(X)) 52.81/14.30 U31(mark(X1), X2) -> mark(U31(X1, X2)) 52.81/14.30 U32(mark(X1), X2) -> mark(U32(X1, X2)) 52.81/14.30 U33(mark(X)) -> mark(U33(X)) 52.81/14.30 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 52.81/14.30 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 52.81/14.30 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 52.81/14.30 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 52.81/14.30 U45(mark(X1), X2) -> mark(U45(X1, X2)) 52.81/14.30 U46(mark(X)) -> mark(U46(X)) 52.81/14.30 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 52.81/14.30 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 52.81/14.30 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 52.81/14.30 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 52.81/14.30 U55(mark(X1), X2) -> mark(U55(X1, X2)) 52.81/14.30 U56(mark(X)) -> mark(U56(X)) 52.81/14.30 U61(mark(X1), X2) -> mark(U61(X1, X2)) 52.81/14.30 U62(mark(X1), X2) -> mark(U62(X1, X2)) 52.81/14.30 U63(mark(X)) -> mark(U63(X)) 52.81/14.30 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 52.81/14.30 U72(mark(X1), X2) -> mark(U72(X1, X2)) 52.81/14.30 U73(mark(X1), X2) -> mark(U73(X1, X2)) 52.81/14.30 U74(mark(X)) -> mark(U74(X)) 52.81/14.30 U81(mark(X1), X2) -> mark(U81(X1, X2)) 52.81/14.30 U82(mark(X1), X2) -> mark(U82(X1, X2)) 52.81/14.30 U83(mark(X)) -> mark(U83(X)) 52.81/14.30 U91(mark(X1), X2) -> mark(U91(X1, X2)) 52.81/14.30 U92(mark(X)) -> mark(U92(X)) 52.81/14.30 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 52.81/14.30 proper(isPalListKind(X)) -> isPalListKind(proper(X)) 52.81/14.30 proper(U13(X)) -> U13(proper(X)) 52.81/14.30 proper(isNeList(X)) -> isNeList(proper(X)) 52.81/14.30 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U24(X1, X2, X3)) -> U24(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U25(X1, X2)) -> U25(proper(X1), proper(X2)) 52.81/14.30 proper(isList(X)) -> isList(proper(X)) 52.81/14.30 proper(U26(X)) -> U26(proper(X)) 52.81/14.30 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 52.81/14.30 proper(U32(X1, X2)) -> U32(proper(X1), proper(X2)) 52.81/14.30 proper(U33(X)) -> U33(proper(X)) 52.81/14.30 proper(isQid(X)) -> isQid(proper(X)) 52.81/14.30 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 52.81/14.30 proper(U46(X)) -> U46(proper(X)) 52.81/14.30 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 52.81/14.30 proper(U56(X)) -> U56(proper(X)) 52.81/14.30 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 52.81/14.30 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 52.81/14.30 proper(U63(X)) -> U63(proper(X)) 52.81/14.30 proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 52.81/14.30 proper(U73(X1, X2)) -> U73(proper(X1), proper(X2)) 52.81/14.30 proper(isPal(X)) -> isPal(proper(X)) 52.81/14.30 proper(U74(X)) -> U74(proper(X)) 52.81/14.30 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 52.81/14.30 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 52.81/14.30 proper(U83(X)) -> U83(proper(X)) 52.81/14.30 proper(isNePal(X)) -> isNePal(proper(X)) 52.81/14.30 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 52.81/14.30 proper(U92(X)) -> U92(proper(X)) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 52.81/14.30 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 52.81/14.30 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 52.81/14.30 isPalListKind(ok(X)) -> ok(isPalListKind(X)) 52.81/14.30 U13(ok(X)) -> ok(U13(X)) 52.81/14.30 isNeList(ok(X)) -> ok(isNeList(X)) 52.81/14.30 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 52.81/14.30 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 52.81/14.30 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 52.81/14.30 U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3)) 52.81/14.30 U25(ok(X1), ok(X2)) -> ok(U25(X1, X2)) 52.81/14.30 isList(ok(X)) -> ok(isList(X)) 52.81/14.30 U26(ok(X)) -> ok(U26(X)) 52.81/14.30 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 52.81/14.30 U32(ok(X1), ok(X2)) -> ok(U32(X1, X2)) 52.81/14.30 U33(ok(X)) -> ok(U33(X)) 52.81/14.30 isQid(ok(X)) -> ok(isQid(X)) 52.81/14.30 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 52.81/14.30 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 52.81/14.30 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 52.81/14.30 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 52.81/14.30 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 52.81/14.30 U46(ok(X)) -> ok(U46(X)) 52.81/14.30 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 52.81/14.30 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 52.81/14.30 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 52.81/14.30 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 52.81/14.30 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 52.81/14.30 U56(ok(X)) -> ok(U56(X)) 52.81/14.30 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 52.81/14.30 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 52.81/14.30 U63(ok(X)) -> ok(U63(X)) 52.81/14.30 U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)) 52.81/14.30 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 52.81/14.30 U73(ok(X1), ok(X2)) -> ok(U73(X1, X2)) 52.81/14.30 isPal(ok(X)) -> ok(isPal(X)) 52.81/14.30 U74(ok(X)) -> ok(U74(X)) 52.81/14.30 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 52.81/14.30 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 52.81/14.30 U83(ok(X)) -> ok(U83(X)) 52.81/14.30 isNePal(ok(X)) -> ok(isNePal(X)) 52.81/14.30 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 52.81/14.30 U92(ok(X)) -> ok(U92(X)) 52.81/14.30 top(mark(X)) -> top(proper(X)) 52.81/14.30 top(ok(X)) -> top(active(X)) 52.81/14.30 52.81/14.30 S is empty. 52.81/14.30 Rewrite Strategy: FULL 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (21) DecreasingLoopProof (LOWER BOUND(ID)) 52.81/14.30 The following loop(s) give(s) rise to the lower bound Omega(n^1): 52.81/14.30 52.81/14.30 The rewrite sequence 52.81/14.30 52.81/14.30 isNePal(ok(X)) ->^+ ok(isNePal(X)) 52.81/14.30 52.81/14.30 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 52.81/14.30 52.81/14.30 The pumping substitution is [X / ok(X)]. 52.81/14.30 52.81/14.30 The result substitution is [ ]. 52.81/14.30 52.81/14.30 52.81/14.30 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (22) 52.81/14.30 Complex Obligation (BEST) 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (23) 52.81/14.30 Obligation: 52.81/14.30 Proved the lower bound n^1 for the following obligation: 52.81/14.30 52.81/14.30 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 52.81/14.30 52.81/14.30 52.81/14.30 The TRS R consists of the following rules: 52.81/14.30 52.81/14.30 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 52.81/14.30 active(__(X, nil)) -> mark(X) 52.81/14.30 active(__(nil, X)) -> mark(X) 52.81/14.30 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 52.81/14.30 active(U12(tt, V)) -> mark(U13(isNeList(V))) 52.81/14.30 active(U13(tt)) -> mark(tt) 52.81/14.30 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 52.81/14.30 active(U25(tt, V2)) -> mark(U26(isList(V2))) 52.81/14.30 active(U26(tt)) -> mark(tt) 52.81/14.30 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 52.81/14.30 active(U32(tt, V)) -> mark(U33(isQid(V))) 52.81/14.30 active(U33(tt)) -> mark(tt) 52.81/14.30 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 52.81/14.30 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 52.81/14.30 active(U46(tt)) -> mark(tt) 52.81/14.30 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 52.81/14.30 active(U55(tt, V2)) -> mark(U56(isList(V2))) 52.81/14.30 active(U56(tt)) -> mark(tt) 52.81/14.30 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 52.81/14.30 active(U62(tt, V)) -> mark(U63(isQid(V))) 52.81/14.30 active(U63(tt)) -> mark(tt) 52.81/14.30 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 52.81/14.30 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 52.81/14.30 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 52.81/14.30 active(U74(tt)) -> mark(tt) 52.81/14.30 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 52.81/14.30 active(U82(tt, V)) -> mark(U83(isNePal(V))) 52.81/14.30 active(U83(tt)) -> mark(tt) 52.81/14.30 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 52.81/14.30 active(U92(tt)) -> mark(tt) 52.81/14.30 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 52.81/14.30 active(isList(nil)) -> mark(tt) 52.81/14.30 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 52.81/14.30 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 52.81/14.30 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 52.81/14.30 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 52.81/14.30 active(isPal(nil)) -> mark(tt) 52.81/14.30 active(isPalListKind(a)) -> mark(tt) 52.81/14.30 active(isPalListKind(e)) -> mark(tt) 52.81/14.30 active(isPalListKind(i)) -> mark(tt) 52.81/14.30 active(isPalListKind(nil)) -> mark(tt) 52.81/14.30 active(isPalListKind(o)) -> mark(tt) 52.81/14.30 active(isPalListKind(u)) -> mark(tt) 52.81/14.30 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 52.81/14.30 active(isQid(a)) -> mark(tt) 52.81/14.30 active(isQid(e)) -> mark(tt) 52.81/14.30 active(isQid(i)) -> mark(tt) 52.81/14.30 active(isQid(o)) -> mark(tt) 52.81/14.30 active(isQid(u)) -> mark(tt) 52.81/14.30 active(__(X1, X2)) -> __(active(X1), X2) 52.81/14.30 active(__(X1, X2)) -> __(X1, active(X2)) 52.81/14.30 active(U11(X1, X2)) -> U11(active(X1), X2) 52.81/14.30 active(U12(X1, X2)) -> U12(active(X1), X2) 52.81/14.30 active(U13(X)) -> U13(active(X)) 52.81/14.30 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 52.81/14.30 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 52.81/14.30 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 52.81/14.30 active(U24(X1, X2, X3)) -> U24(active(X1), X2, X3) 52.81/14.30 active(U25(X1, X2)) -> U25(active(X1), X2) 52.81/14.30 active(U26(X)) -> U26(active(X)) 52.81/14.30 active(U31(X1, X2)) -> U31(active(X1), X2) 52.81/14.30 active(U32(X1, X2)) -> U32(active(X1), X2) 52.81/14.30 active(U33(X)) -> U33(active(X)) 52.81/14.30 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 52.81/14.30 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 52.81/14.30 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 52.81/14.30 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 52.81/14.30 active(U45(X1, X2)) -> U45(active(X1), X2) 52.81/14.30 active(U46(X)) -> U46(active(X)) 52.81/14.30 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 52.81/14.30 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 52.81/14.30 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 52.81/14.30 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 52.81/14.30 active(U55(X1, X2)) -> U55(active(X1), X2) 52.81/14.30 active(U56(X)) -> U56(active(X)) 52.81/14.30 active(U61(X1, X2)) -> U61(active(X1), X2) 52.81/14.30 active(U62(X1, X2)) -> U62(active(X1), X2) 52.81/14.30 active(U63(X)) -> U63(active(X)) 52.81/14.30 active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) 52.81/14.30 active(U72(X1, X2)) -> U72(active(X1), X2) 52.81/14.30 active(U73(X1, X2)) -> U73(active(X1), X2) 52.81/14.30 active(U74(X)) -> U74(active(X)) 52.81/14.30 active(U81(X1, X2)) -> U81(active(X1), X2) 52.81/14.30 active(U82(X1, X2)) -> U82(active(X1), X2) 52.81/14.30 active(U83(X)) -> U83(active(X)) 52.81/14.30 active(U91(X1, X2)) -> U91(active(X1), X2) 52.81/14.30 active(U92(X)) -> U92(active(X)) 52.81/14.30 __(mark(X1), X2) -> mark(__(X1, X2)) 52.81/14.30 __(X1, mark(X2)) -> mark(__(X1, X2)) 52.81/14.30 U11(mark(X1), X2) -> mark(U11(X1, X2)) 52.81/14.30 U12(mark(X1), X2) -> mark(U12(X1, X2)) 52.81/14.30 U13(mark(X)) -> mark(U13(X)) 52.81/14.30 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 52.81/14.30 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 52.81/14.30 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 52.81/14.30 U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3)) 52.81/14.30 U25(mark(X1), X2) -> mark(U25(X1, X2)) 52.81/14.30 U26(mark(X)) -> mark(U26(X)) 52.81/14.30 U31(mark(X1), X2) -> mark(U31(X1, X2)) 52.81/14.30 U32(mark(X1), X2) -> mark(U32(X1, X2)) 52.81/14.30 U33(mark(X)) -> mark(U33(X)) 52.81/14.30 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 52.81/14.30 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 52.81/14.30 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 52.81/14.30 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 52.81/14.30 U45(mark(X1), X2) -> mark(U45(X1, X2)) 52.81/14.30 U46(mark(X)) -> mark(U46(X)) 52.81/14.30 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 52.81/14.30 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 52.81/14.30 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 52.81/14.30 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 52.81/14.30 U55(mark(X1), X2) -> mark(U55(X1, X2)) 52.81/14.30 U56(mark(X)) -> mark(U56(X)) 52.81/14.30 U61(mark(X1), X2) -> mark(U61(X1, X2)) 52.81/14.30 U62(mark(X1), X2) -> mark(U62(X1, X2)) 52.81/14.30 U63(mark(X)) -> mark(U63(X)) 52.81/14.30 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 52.81/14.30 U72(mark(X1), X2) -> mark(U72(X1, X2)) 52.81/14.30 U73(mark(X1), X2) -> mark(U73(X1, X2)) 52.81/14.30 U74(mark(X)) -> mark(U74(X)) 52.81/14.30 U81(mark(X1), X2) -> mark(U81(X1, X2)) 52.81/14.30 U82(mark(X1), X2) -> mark(U82(X1, X2)) 52.81/14.30 U83(mark(X)) -> mark(U83(X)) 52.81/14.30 U91(mark(X1), X2) -> mark(U91(X1, X2)) 52.81/14.30 U92(mark(X)) -> mark(U92(X)) 52.81/14.30 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 52.81/14.30 proper(isPalListKind(X)) -> isPalListKind(proper(X)) 52.81/14.30 proper(U13(X)) -> U13(proper(X)) 52.81/14.30 proper(isNeList(X)) -> isNeList(proper(X)) 52.81/14.30 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U24(X1, X2, X3)) -> U24(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U25(X1, X2)) -> U25(proper(X1), proper(X2)) 52.81/14.30 proper(isList(X)) -> isList(proper(X)) 52.81/14.30 proper(U26(X)) -> U26(proper(X)) 52.81/14.30 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 52.81/14.30 proper(U32(X1, X2)) -> U32(proper(X1), proper(X2)) 52.81/14.30 proper(U33(X)) -> U33(proper(X)) 52.81/14.30 proper(isQid(X)) -> isQid(proper(X)) 52.81/14.30 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 52.81/14.30 proper(U46(X)) -> U46(proper(X)) 52.81/14.30 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 52.81/14.30 proper(U56(X)) -> U56(proper(X)) 52.81/14.30 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 52.81/14.30 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 52.81/14.30 proper(U63(X)) -> U63(proper(X)) 52.81/14.30 proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 52.81/14.30 proper(U73(X1, X2)) -> U73(proper(X1), proper(X2)) 52.81/14.30 proper(isPal(X)) -> isPal(proper(X)) 52.81/14.30 proper(U74(X)) -> U74(proper(X)) 52.81/14.30 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 52.81/14.30 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 52.81/14.30 proper(U83(X)) -> U83(proper(X)) 52.81/14.30 proper(isNePal(X)) -> isNePal(proper(X)) 52.81/14.30 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 52.81/14.30 proper(U92(X)) -> U92(proper(X)) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 52.81/14.30 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 52.81/14.30 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 52.81/14.30 isPalListKind(ok(X)) -> ok(isPalListKind(X)) 52.81/14.30 U13(ok(X)) -> ok(U13(X)) 52.81/14.30 isNeList(ok(X)) -> ok(isNeList(X)) 52.81/14.30 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 52.81/14.30 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 52.81/14.30 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 52.81/14.30 U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3)) 52.81/14.30 U25(ok(X1), ok(X2)) -> ok(U25(X1, X2)) 52.81/14.30 isList(ok(X)) -> ok(isList(X)) 52.81/14.30 U26(ok(X)) -> ok(U26(X)) 52.81/14.30 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 52.81/14.30 U32(ok(X1), ok(X2)) -> ok(U32(X1, X2)) 52.81/14.30 U33(ok(X)) -> ok(U33(X)) 52.81/14.30 isQid(ok(X)) -> ok(isQid(X)) 52.81/14.30 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 52.81/14.30 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 52.81/14.30 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 52.81/14.30 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 52.81/14.30 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 52.81/14.30 U46(ok(X)) -> ok(U46(X)) 52.81/14.30 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 52.81/14.30 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 52.81/14.30 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 52.81/14.30 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 52.81/14.30 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 52.81/14.30 U56(ok(X)) -> ok(U56(X)) 52.81/14.30 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 52.81/14.30 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 52.81/14.30 U63(ok(X)) -> ok(U63(X)) 52.81/14.30 U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)) 52.81/14.30 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 52.81/14.30 U73(ok(X1), ok(X2)) -> ok(U73(X1, X2)) 52.81/14.30 isPal(ok(X)) -> ok(isPal(X)) 52.81/14.30 U74(ok(X)) -> ok(U74(X)) 52.81/14.30 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 52.81/14.30 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 52.81/14.30 U83(ok(X)) -> ok(U83(X)) 52.81/14.30 isNePal(ok(X)) -> ok(isNePal(X)) 52.81/14.30 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 52.81/14.30 U92(ok(X)) -> ok(U92(X)) 52.81/14.30 top(mark(X)) -> top(proper(X)) 52.81/14.30 top(ok(X)) -> top(active(X)) 52.81/14.30 52.81/14.30 S is empty. 52.81/14.30 Rewrite Strategy: FULL 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (24) LowerBoundPropagationProof (FINISHED) 52.81/14.30 Propagated lower bound. 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (25) 52.81/14.30 BOUNDS(n^1, INF) 52.81/14.30 52.81/14.30 ---------------------------------------- 52.81/14.30 52.81/14.30 (26) 52.81/14.30 Obligation: 52.81/14.30 Analyzing the following TRS for decreasing loops: 52.81/14.30 52.81/14.30 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 52.81/14.30 52.81/14.30 52.81/14.30 The TRS R consists of the following rules: 52.81/14.30 52.81/14.30 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 52.81/14.30 active(__(X, nil)) -> mark(X) 52.81/14.30 active(__(nil, X)) -> mark(X) 52.81/14.30 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 52.81/14.30 active(U12(tt, V)) -> mark(U13(isNeList(V))) 52.81/14.30 active(U13(tt)) -> mark(tt) 52.81/14.30 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 52.81/14.30 active(U25(tt, V2)) -> mark(U26(isList(V2))) 52.81/14.30 active(U26(tt)) -> mark(tt) 52.81/14.30 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 52.81/14.30 active(U32(tt, V)) -> mark(U33(isQid(V))) 52.81/14.30 active(U33(tt)) -> mark(tt) 52.81/14.30 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 52.81/14.30 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 52.81/14.30 active(U46(tt)) -> mark(tt) 52.81/14.30 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 52.81/14.30 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 52.81/14.30 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 52.81/14.30 active(U55(tt, V2)) -> mark(U56(isList(V2))) 52.81/14.30 active(U56(tt)) -> mark(tt) 52.81/14.30 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 52.81/14.30 active(U62(tt, V)) -> mark(U63(isQid(V))) 52.81/14.30 active(U63(tt)) -> mark(tt) 52.81/14.30 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 52.81/14.30 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 52.81/14.30 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 52.81/14.30 active(U74(tt)) -> mark(tt) 52.81/14.30 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 52.81/14.30 active(U82(tt, V)) -> mark(U83(isNePal(V))) 52.81/14.30 active(U83(tt)) -> mark(tt) 52.81/14.30 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 52.81/14.30 active(U92(tt)) -> mark(tt) 52.81/14.30 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 52.81/14.30 active(isList(nil)) -> mark(tt) 52.81/14.30 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 52.81/14.30 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 52.81/14.30 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 52.81/14.30 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 52.81/14.30 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 52.81/14.30 active(isPal(nil)) -> mark(tt) 52.81/14.30 active(isPalListKind(a)) -> mark(tt) 52.81/14.30 active(isPalListKind(e)) -> mark(tt) 52.81/14.30 active(isPalListKind(i)) -> mark(tt) 52.81/14.30 active(isPalListKind(nil)) -> mark(tt) 52.81/14.30 active(isPalListKind(o)) -> mark(tt) 52.81/14.30 active(isPalListKind(u)) -> mark(tt) 52.81/14.30 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 52.81/14.30 active(isQid(a)) -> mark(tt) 52.81/14.30 active(isQid(e)) -> mark(tt) 52.81/14.30 active(isQid(i)) -> mark(tt) 52.81/14.30 active(isQid(o)) -> mark(tt) 52.81/14.30 active(isQid(u)) -> mark(tt) 52.81/14.30 active(__(X1, X2)) -> __(active(X1), X2) 52.81/14.30 active(__(X1, X2)) -> __(X1, active(X2)) 52.81/14.30 active(U11(X1, X2)) -> U11(active(X1), X2) 52.81/14.30 active(U12(X1, X2)) -> U12(active(X1), X2) 52.81/14.30 active(U13(X)) -> U13(active(X)) 52.81/14.30 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 52.81/14.30 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 52.81/14.30 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 52.81/14.30 active(U24(X1, X2, X3)) -> U24(active(X1), X2, X3) 52.81/14.30 active(U25(X1, X2)) -> U25(active(X1), X2) 52.81/14.30 active(U26(X)) -> U26(active(X)) 52.81/14.30 active(U31(X1, X2)) -> U31(active(X1), X2) 52.81/14.30 active(U32(X1, X2)) -> U32(active(X1), X2) 52.81/14.30 active(U33(X)) -> U33(active(X)) 52.81/14.30 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 52.81/14.30 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 52.81/14.30 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 52.81/14.30 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 52.81/14.30 active(U45(X1, X2)) -> U45(active(X1), X2) 52.81/14.30 active(U46(X)) -> U46(active(X)) 52.81/14.30 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 52.81/14.30 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 52.81/14.30 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 52.81/14.30 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 52.81/14.30 active(U55(X1, X2)) -> U55(active(X1), X2) 52.81/14.30 active(U56(X)) -> U56(active(X)) 52.81/14.30 active(U61(X1, X2)) -> U61(active(X1), X2) 52.81/14.30 active(U62(X1, X2)) -> U62(active(X1), X2) 52.81/14.30 active(U63(X)) -> U63(active(X)) 52.81/14.30 active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) 52.81/14.30 active(U72(X1, X2)) -> U72(active(X1), X2) 52.81/14.30 active(U73(X1, X2)) -> U73(active(X1), X2) 52.81/14.30 active(U74(X)) -> U74(active(X)) 52.81/14.30 active(U81(X1, X2)) -> U81(active(X1), X2) 52.81/14.30 active(U82(X1, X2)) -> U82(active(X1), X2) 52.81/14.30 active(U83(X)) -> U83(active(X)) 52.81/14.30 active(U91(X1, X2)) -> U91(active(X1), X2) 52.81/14.30 active(U92(X)) -> U92(active(X)) 52.81/14.30 __(mark(X1), X2) -> mark(__(X1, X2)) 52.81/14.30 __(X1, mark(X2)) -> mark(__(X1, X2)) 52.81/14.30 U11(mark(X1), X2) -> mark(U11(X1, X2)) 52.81/14.30 U12(mark(X1), X2) -> mark(U12(X1, X2)) 52.81/14.30 U13(mark(X)) -> mark(U13(X)) 52.81/14.30 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 52.81/14.30 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 52.81/14.30 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 52.81/14.30 U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3)) 52.81/14.30 U25(mark(X1), X2) -> mark(U25(X1, X2)) 52.81/14.30 U26(mark(X)) -> mark(U26(X)) 52.81/14.30 U31(mark(X1), X2) -> mark(U31(X1, X2)) 52.81/14.30 U32(mark(X1), X2) -> mark(U32(X1, X2)) 52.81/14.30 U33(mark(X)) -> mark(U33(X)) 52.81/14.30 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 52.81/14.30 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 52.81/14.30 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 52.81/14.30 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 52.81/14.30 U45(mark(X1), X2) -> mark(U45(X1, X2)) 52.81/14.30 U46(mark(X)) -> mark(U46(X)) 52.81/14.30 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 52.81/14.30 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 52.81/14.30 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 52.81/14.30 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 52.81/14.30 U55(mark(X1), X2) -> mark(U55(X1, X2)) 52.81/14.30 U56(mark(X)) -> mark(U56(X)) 52.81/14.30 U61(mark(X1), X2) -> mark(U61(X1, X2)) 52.81/14.30 U62(mark(X1), X2) -> mark(U62(X1, X2)) 52.81/14.30 U63(mark(X)) -> mark(U63(X)) 52.81/14.30 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 52.81/14.30 U72(mark(X1), X2) -> mark(U72(X1, X2)) 52.81/14.30 U73(mark(X1), X2) -> mark(U73(X1, X2)) 52.81/14.30 U74(mark(X)) -> mark(U74(X)) 52.81/14.30 U81(mark(X1), X2) -> mark(U81(X1, X2)) 52.81/14.30 U82(mark(X1), X2) -> mark(U82(X1, X2)) 52.81/14.30 U83(mark(X)) -> mark(U83(X)) 52.81/14.30 U91(mark(X1), X2) -> mark(U91(X1, X2)) 52.81/14.30 U92(mark(X)) -> mark(U92(X)) 52.81/14.30 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 52.81/14.30 proper(nil) -> ok(nil) 52.81/14.30 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 52.81/14.30 proper(tt) -> ok(tt) 52.81/14.30 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 52.81/14.30 proper(isPalListKind(X)) -> isPalListKind(proper(X)) 52.81/14.30 proper(U13(X)) -> U13(proper(X)) 52.81/14.30 proper(isNeList(X)) -> isNeList(proper(X)) 52.81/14.30 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U24(X1, X2, X3)) -> U24(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U25(X1, X2)) -> U25(proper(X1), proper(X2)) 52.81/14.30 proper(isList(X)) -> isList(proper(X)) 52.81/14.30 proper(U26(X)) -> U26(proper(X)) 52.81/14.30 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 52.81/14.30 proper(U32(X1, X2)) -> U32(proper(X1), proper(X2)) 52.81/14.30 proper(U33(X)) -> U33(proper(X)) 52.81/14.30 proper(isQid(X)) -> isQid(proper(X)) 52.81/14.30 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 52.81/14.30 proper(U46(X)) -> U46(proper(X)) 52.81/14.30 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 52.81/14.30 proper(U56(X)) -> U56(proper(X)) 52.81/14.30 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 52.81/14.30 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 52.81/14.30 proper(U63(X)) -> U63(proper(X)) 52.81/14.30 proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)) 52.81/14.30 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 52.81/14.30 proper(U73(X1, X2)) -> U73(proper(X1), proper(X2)) 52.81/14.30 proper(isPal(X)) -> isPal(proper(X)) 52.81/14.30 proper(U74(X)) -> U74(proper(X)) 52.81/14.30 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 52.81/14.30 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 52.81/14.30 proper(U83(X)) -> U83(proper(X)) 52.81/14.30 proper(isNePal(X)) -> isNePal(proper(X)) 52.81/14.30 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 52.81/14.30 proper(U92(X)) -> U92(proper(X)) 52.81/14.30 proper(a) -> ok(a) 52.81/14.30 proper(e) -> ok(e) 52.81/14.30 proper(i) -> ok(i) 52.81/14.30 proper(o) -> ok(o) 52.81/14.30 proper(u) -> ok(u) 52.81/14.30 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 52.81/14.30 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 52.81/14.30 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 52.81/14.30 isPalListKind(ok(X)) -> ok(isPalListKind(X)) 52.81/14.30 U13(ok(X)) -> ok(U13(X)) 52.81/14.30 isNeList(ok(X)) -> ok(isNeList(X)) 52.81/14.30 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 52.81/14.30 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 52.81/14.30 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 52.81/14.30 U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3)) 52.81/14.30 U25(ok(X1), ok(X2)) -> ok(U25(X1, X2)) 52.81/14.30 isList(ok(X)) -> ok(isList(X)) 52.81/14.30 U26(ok(X)) -> ok(U26(X)) 52.81/14.30 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 52.81/14.30 U32(ok(X1), ok(X2)) -> ok(U32(X1, X2)) 52.81/14.30 U33(ok(X)) -> ok(U33(X)) 52.81/14.30 isQid(ok(X)) -> ok(isQid(X)) 52.81/14.30 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 52.81/14.30 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 52.81/14.30 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 52.81/14.30 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 52.81/14.30 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 52.81/14.30 U46(ok(X)) -> ok(U46(X)) 52.81/14.30 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 52.81/14.30 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 52.81/14.30 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 52.81/14.30 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 52.81/14.30 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 52.81/14.30 U56(ok(X)) -> ok(U56(X)) 52.81/14.30 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 52.81/14.30 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 52.81/14.30 U63(ok(X)) -> ok(U63(X)) 52.81/14.30 U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3)) 52.81/14.30 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 52.81/14.30 U73(ok(X1), ok(X2)) -> ok(U73(X1, X2)) 52.81/14.30 isPal(ok(X)) -> ok(isPal(X)) 52.81/14.30 U74(ok(X)) -> ok(U74(X)) 52.81/14.30 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 52.81/14.30 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 52.81/14.30 U83(ok(X)) -> ok(U83(X)) 52.81/14.30 isNePal(ok(X)) -> ok(isNePal(X)) 52.81/14.30 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 52.81/14.30 U92(ok(X)) -> ok(U92(X)) 52.81/14.30 top(mark(X)) -> top(proper(X)) 52.81/14.30 top(ok(X)) -> top(active(X)) 52.81/14.30 52.81/14.30 S is empty. 52.81/14.30 Rewrite Strategy: FULL 53.07/14.36 EOF